* place lilyglyphs.sty and the complete definitions/ folder somewhere
on your disk, e.g. in a directory ~/lilyglyphs.
* create symlinks to lilyglyphs.sty and the definitions/ folder _in
the directory_ where your .tex file is located:
ln -s ~/lilyglyphs/lilyglyphs.sty
ln -s ~/lilyglyphs/definitions
-> This is going to pretend that the package is in the same dir as
your .tex file.
Alternatively you can (for testing the package) put your .tex file
in the directory where lilyglyphs.sty is.
Ouch. Why not simply put it into your local TEXMF folder, usually
~/texmf? Then you don't have to do any further links! If it doesn't
exist yet, you should create it. An appropiate subdirectory is
~/texmf/tex/xelatex/lilyglyphs/