I got it myself after a lot of trying and comparing:

In my file gnuplot.xtemplate I wrote "InputFormat gp", because
"InputFormat" and FileFilter extension are the same in the case of Xfig
(fig) and Inkscape (svg), but not with gnuplot: "InputFormat gnuplot"
and FileFilter .gp works!

For anyone interested I attached my working gnuplot.xtemplate. 

Sorry for making noise!

Tobias


Am Samstag, dem 20.04.2024 um 08:44 +0200 schrieb Tobias Hilbricht:
> Dear LyX-user,
> 
> I would like to have a gnuplot xtemplate. To that end I wrote a shell
> script gnuplot2pdftex.sh like this:
> 
> #!/bin/bash
> GnuplotFile=$1
> BaseName=`basename $GnuplotFile .gp`
> GnuplotName=$BaseName.ptx
> LyxName=$BaseName.pdf_tex
> gnuplot -e "set term cairolatex pdf ; set output '${GnuplotName}' "
> $GnuplotFile
> mv $GnuplotName $LyxName
> 
> This script works on the command line, and I can input the resulting
> file gnuplot.pdf_tex in LyX, and if I put it in a preview box I get a
> preview, and the document compiles.
> 
> I have similar scripts for pstex, png and eps in
> ~/.lyx/scripts and define converters like this:
> 
> \converter "gnuplot" "pdftex2" "$$s/scripts/gnuplot2pdftex.sh $$i
> $$o"
> "needauth"
> 
> and have a file gnuplot.xtemplate written after the model of
> inkscape.xtemplate in ~/.lyx/xtemplate
#
# Gnuplot External Template
#
# This file is part of LyX, the document processor.
# Licence details can be found in the file COPYING.
#
# author Tobias Hilbricht
#
# based on external templates by:
#
# author Asger Alstrup Nielsen
# author Angus Leeming
# author Johnathan Burchill
#
# Full author contact details are available in file CREDITS.


PreambleDef WarnNotFound
        %% Print a warning encased in an fbox.
        \def\lyxstripprefix#1>{}
        \newcommand{\warnNotFound}[1]{%
                \def\lyxtempfilename{#1}%
                \fbox{Could not find
                        
\ttfamily\expandafter\lyxstripprefix\meaning\lyxtempfilename!}%
                \typeout{Could not find \lyxtempfilename!}%
        }
PreambleDefEnd


PreambleDef InputOrWarn
        %% Input the file if it exists, using \input, else print a warning
        \newcommand{\inputOrWarn}[1]{%
                \IfFileExists{#1}{\input{#1}}{\warnNotFound{#1}}}
PreambleDefEnd


Template Gnuplot
        GuiName "Gnuplot"
        HelpText
                A Gnuplot figure.
                Note that using this template automatically uses the 
                document text in the image (like with the Xfig template).
        HelpTextEnd
        InputFormat gnuplot
        FileFilter "*.{gp}"
        AutomaticProduction true
        Transform Rotate
        Transform Resize
        Preview InstantPreview
        Format PDFLaTeX
                TransformCommand Rotate RotationLatexCommand
                TransformCommand Resize ResizeLatexCommand
                Product 
"$$RotateFront$$ResizeFront\\input{$$AbsOrRelPathMaster$$Basename.pdf_tex}$$ResizeBack$$RotateBack"
                UpdateFormat pdftex2
                UpdateResult "$$AbsPath$$Basename.pdf_tex"
                Requirement "xcolor"
                Requirement "graphicx"
                Requirement "mathtools"
                # Preamble WarnNotFound
                # Preamble InputOrWarn
                ReferencedFile pdflatex "$$AbsOrRelPathMaster$$Basename.pdf_tex"
                ReferencedFile pdflatex "$$AbsPath$$Basename.pdf"
        FormatEnd
        Format LaTeX
                TransformCommand Rotate RotationLatexCommand
                TransformCommand Resize ResizeLatexCommand
                Product 
"$$RotateFront$$ResizeFront\\input{$$AbsOrRelPathMaster$$Basename.ps_tex}$$ResizeBack$$RotateBack"
                UpdateFormat pstex2
                UpdateResult "$$AbsPath$$Basename.ps_tex"
                Requirement "xcolor"
                Requirement "graphicx"
                Requirement "mathtools"
                # Preamble WarnNotFound
                # Preamble InputOrWarn
                ReferencedFile latex "$$AbsOrRelPathMaster$$Basename.ps_tex"
                ReferencedFile latex "$$AbsPath$$Basename.eps"
                ReferencedFile dvi   "$$AbsPath$$Basename.eps"
        FormatEnd
        Format Ascii
                Product "[InkscapeGraphics: $$FName]"
        FormatEnd
        Format DocBook
                Product "<graphic 
fileref=\"$$AbsOrRelPathMaster$$Basename.eps\"></graphic>"
                UpdateFormat eps
                UpdateResult "$$AbsPath$$Basename.eps"
                ReferencedFile docbook     "$$AbsPath$$Basename.eps"
                ReferencedFile docbook-xml "$$AbsPath$$Basename.eps"
        FormatEnd
        Format XHTML
                Product "<img src=\"$$AbsOrRelPathMaster$$Basename.svg\" />"
                UpdateFormat svg
                UpdateResult "$$AbsPath$$Basename.svg"
                ReferencedFile xhtml "$$AbsPath$$Basename.svg"
        FormatEnd
TemplateEnd

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