Using GNOME

In GNOME, URIs are handled via ‘.desktop’ files. Create a file in a local directory such as /tmp that is called lilypond-invoke-editor.desktop and has the contents;

[Desktop Entry]
Version=1.0
Name=lilypond-invoke-editor
GenericName=Textedit URI handler
Comment=URI handler for textedit:
Exec=lilypond-invoke-editor %u
Terminal=false
Type=Application
MimeType=x-scheme-handler/textedit;
Categories=Editor
NoDisplay=true

and then execute the commands

xdg-desktop-menu install ./lilypond-invoke-editor.desktop
xdg-mime default lilypond-invoke-editor.desktop x-scheme-handler/textedit

After that invocation;

xdg-open textedit:///etc/issue:1:0:0

should call lilypond-invoke-editor for opening files.

LilyPond Application Usage v2.25.22 (development-branch).