> I'm just wondering if it's possible in Lilypond to create a table of
> contents that is alphabetical by item, rather than by page number
> order?

IMHO this is not a table of context but rather an index that is
positioned near the beginning.

> I'm trying to create an alphabetical index by hymn tune or first
> line that will go in the back of a book.

I suggest to not do this in directly in LilyPond.[*] With
`lilypond-book` in LaTeX mode, for example, you might read this link,
which covers *exactly* your use-case:

  https://latex.org/forum/viewtopic.php?t=4169


    Werner


[*] Except Jean has time and interest to produce a solution like pulling
    a rabbit out of a hat :-)

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