Hi,

First of all, I have to admit that I know almost nothing about those type
of chants.
Anyway...
AFAIK, there is no predefined context or commands that will do - exactly -
such scores.
I've done something similar on the german forum :
http://www.lilypondforum.de/index.php?topic=1801.msg9962#msg9962
The main idea was to put one voice per grouped note.

In your particular case it does not seem to be a good idea; So please find
attached a compilable file :
1. I've tried to stick as much as possible to your original pdf.
2. the idea was to change the note heads stencil with grouped notes - with
or without stems, spaces and/or ornaments.
3. not easy...

Hope you'll find better and/or easier solution.

Cheers,
Pierre
\version "2.18.2"
%\pointAndClickOff

%% Works with other sizes:
%#(set-global-staff-size 25)

\paper { 
  indent = 0
  top-margin = 15
  left-margin = 20
  right-margin = 20
  tagline = ##f
}

\header {
  title = \markup { \bold "4b." \normal-text "XV. zsoltár" }
}
\markup\vspace #2 % <= put some vertical space here

%%%% Defining new grobs:

%% quater note head:
o = \markup\concat { \hspace #-.1 \musicglyph #"noteheads.s2" }

%% quater note head with ledger line:
ol = \markup\concat { \hspace #-.1 { \musicglyph #"noteheads.s2" \hspace #-1.65 \override #'(thickness . 2.25)\draw-line #'(1.75 . 0) } }

%% strait stem:
st = \markup\concat { \hspace #-.1 \draw-line #'(0 . -3.5) \hspace #-.01 }

%% short curved stem:
svOne = \markup\lower #.7 \fontsize #2 \concat { \hspace #-.85 \scale #'(1 . .5)\char ##x23B1 \hspace #-.7 }

%% medium curved stem:
svTwo = \markup\lower #1.1 \fontsize #2 \concat { \hspace #-.8 \scale #'(1 . .75)\char ##x23B1 \hspace #-.7 }

%% long curved stem:
svThree = \markup\lower #1.55 \fontsize #2 \concat { \hspace #-.8 \scale #'(1 . .9)\char ##x23B1 \hspace #-.7 }

%% ornament:
gr = \markup\concat { \hspace #.4 \lower #1.5 \fontsize #8 \char ##x1D19F }

%% Left aligning lyric :
lal = \once\override LyricText.self-alignment-X = #LEFT

%%%%%%%%%%% Example %%%%%%%%%%%%%%

myMelody = \transpose c c' {
  \clef G
  \cadenzaOn
  d 
  d d 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o % resp. f
               \raise #0.5 \o  % resp. g
               \raise #1 { \st\o } % resp. stem / a
             }
           #}))
  f
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o\gr % resp. g / ornament
           }
         #}))
  g 
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o % resp. g
             \raise #.5 \o  % resp. a
             \raise #1.5 { \st\o } % resp. stem / c'
           }
         #}))
  g 
  a 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \st\o\svOne % resp. stem / a / short curved stem
             \lower #.5 \o % resp. g
             \o % resp. a
             \raise #1 { \st\o\svThree } % resp. stem / c' / long curved stem
             \lower #.5 \o % etc.
             \st\o\svOne
             \lower #.5 { \o\svOne }
             \lower #1 \o
           }
         #}))
  a 
  \bar "'"
  a c' 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \st\o\svOne
             \lower #.5 { \o\svOne }
             \lower #1 \o
           }
         #}))
  c'
  \bar ""\break
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o 
               \raise #0.5 \o 
               \raise #1 { \st\o\svOne }
               \raise #0.5 { \o\svTwo  }
               \lower #0.5 \o
               \lower #0.5 \o
               \o
               \raise #0.5 { \o\svOne }
               \o\svOne
               \lower #0.5 \o
             }
           #}))
  b 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o 
               \raise #0.5 \o 
               \raise #1.5 { \st\o\svTwo }
               \raise #0.5 \o
               \o
               \raise #0.5 { \st\o }
             }
           #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o 
               \raise #0.5 \o 
               \raise #1.5 { \st\o\svTwo }
               \raise #0.5 \o
             }
           #}))
  g 
  \bar "|"
  f 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o 
               \raise #1 { \st\o }
             }
           #}))
  a 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o 
               \raise #.5 { \st\o\svOne }
               \o \hspace #-0.9 \gr
             }
           #}))
  c' 
  c' 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o 
               \raise #.5 { \st\o\svTwo }
               \lower #.5 \o
             }
           #}))
  c'
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o 
               \raise #.5 { \st\o }
             }
           #}))
  c' 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o\svTwo 
               \lower #1 \o
               \lower #0.5 \o
               \st\o
             }
           #}))
  d' 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o % a
             \raise #0.5 \o % b
             \raise #1 { \st\o\svOne } % c'
             \raise #0.5 { \o\svOne } % b
             \o\svOne % a
             \lower #0.5 \o % g
             \st\o % a
           }
         #}))
  a 
  \bar "" \break
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \st\o\svOne
               \lower #0.5 \o
             }
           #}))
  a 
  \bar "'"
  a 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o
               \raise #1 { \st\o\svOne }
               \raise #0.5 { \o\svTwo }
               \lower #0.5 \o
             }
           #}))
  a 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \o\o
             }
           #}))
  c' 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \st\o\svOne
               \lower #0.5 { \o\svOne }
               \lower #1 \o
               \lower #0.5 { \st\o\svTwo }
               \lower #1.5 { \o\svOne }
               \lower #2 \o
             }
           #}))
  d' 
  \once\override NoteHead.stencil = #(lambda (grob)
         (grob-interpret-markup grob 
           #{
             \markup\concat {
               \st\o\svOne
               \lower #0.5 \o
               \st\o\svOne
               \lower #0.5 { \o\svOne }
               \lower #1 \o
               \lower #0.5 { \st\o }
             }
           #}))
  a 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \st\o\svOne
             \lower #0.5 \o
           }
         #}))
  g 
  \bar "|"
  f g a 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 { \st\o }
           }
         #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o\gr
           }
         #}))
  g 
  g
  \bar "" \break
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 { \st\o }
           }
         #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \st\o\svOne
             \lower #0.5 \o
           }
         #}))
  f 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #1.5 { \st\o }
           }
         #}))
  d 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 { \st\o\svTwo }
             \lower #0.5 { \o\svOne }
             \lower #1 { \o\svOne }
             \lower #1.5 \o
           }
         #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #1 { \st\o\svTwo }
             \o\svOne
             \lower #0.5 \ol
             \hspace #0.8
             \o
             \raise #1 { \st\o\svTwo }
             \o
           }
         #}))
  d \bar "'" 
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 { \st\o\svOne }
             \o\svOne
             \lower #0.5 \o
             \o
             \raise #0.5 { \st\o }
           }
         #}))
  g 
  g
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 \o
             \raise #1.5 { \st\o\svTwo }
             \raise #0.5 { \o\o }
             \raise #1 \o
             \raise #1.5 { \st\o\svOne }
             \raise #1 { \o\svOne }
             \raise #0.5 \o
           }
         #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 \o
             \raise #1.5 { \st\o\svTwo }
             \raise #0.5 { \o\svOne }
             \o
             \raise #.5 { \st\o }
           }
         #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \st\o\svOne
             \lower #0.5 \o
           }
         #}))
  a 
  \bar "|." \break
  c' c' c'
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 { \st\o\svOne }
             \o\st\o\svTwo
             \lower #1 { \o\svOne }
             \lower #1.5 \o
           }
         #}))
  c' 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o 
             \raise #1 { \st\o }
           }
         #}))
  a c' \bar "'" c' c' 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
            \o\o
           }
         #}))
  c' 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o 
             \raise #1 { \st\o }
           }
         #}))
  a 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o 
             \raise #0.5 \o
             \raise #1.5 { \st\o\svTwo }
             \raise #0.5 \o
           }
         #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \st\o\svOne
             \lower #0.5 \o 
           }
         #}))
  a 
  \bar "|" 
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o 
             \raise #0.5 { \st\o }
           }
         #}))
  f
  \bar "" \break
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 { \st\o }
           }
         #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o \hspace #.8 \gr
           }
         #}))
  g g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #1 { \st\o\svTwo }
             \o\svOne
             \lower #0.5 \o
             \o
             \raise #1 { \st\o\svTwo }
             \o
           }
         #}))
  a 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 { \st\o\svTwo }
             \lower #0.5 \o
           }
         #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 { \st\o }
           }
         #}))
  g 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #0.5 \o
             \raise #1 \o
             \raise #1.5 { \st\o }
             \raise #1 { \o\st\o\svOne }
             \raise #0.5 { \o\svOne }
             \o
           }
         #}))
  a 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o
             \raise #1 { \st\o\svTwo }
             \o\svOne
             \lower #0.5 \o
             \hspace #1
             \st\o\svOne
             \lower #0.5 \o
           }
         #}))
  a 
  \bar "|." 
  \once\override NoteHead.stencil = #(lambda (grob)
       (grob-interpret-markup grob 
         #{
           \markup\concat {
             \o \hspace #2 
             \raise #1 \o
             \raise #2 { \st\o \hspace #2 \o }
           }
         #}))
  f 
  \bar "|."
}

myLyrics = \lyricmode {
  \set stanza = \markup\box\pad-markup #.5 \bold "4b"
  Meg- is- mer- tet- ted
  % or:
  % Meg -- is -- mer -- tet -- ted
  ve- lem,
  U- \lal ram az é- let
  \lal út- \lal ja- \lal it,
  \set stanza = #"*" 
  \lal be-  töl- tesz
  vi- gas- sá- gal \lal en- 
  gem a te szí- \lal ned \lal e- lőtt
  gyö- nyö- rű- ség- gel a
  te job- bod \lal fe- \lal lől
  ö- \lal rök- kön \lal ö- \lal rök- ké.
  \set stanza = #"V)"
  Tarts meg en- \lal gem,
  U- ram, mert te- ben- ned \lal bíz- tam,
  mon- dám az Úr- nak: 
  én Is- te- \lal nem \lal vagy \lal te.
  \set stanza = #"*"
  \lal
  Betöltesz.
}

\score {
  <<
    \new Voice = MyMelody \myMelody
    \new Lyrics \lyricsto MyMelody \myLyrics
  >>
  \layout {
    \context {
      \Score
      \omit TimeSignature
    }
    \context {
      \Staff
      \omit Stem
    }
    \context {
      \Lyrics
      \override VerticalAxisGroup.staff-affinity = ##f
    }
  }
}
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