thelounge: write out default path for thelounge

The output file is found and handled by thelounge itself [1], leaving
the user free to override THELOUNGE_HOME in the environment if they
choose, but having a sensible default to make `thelounge` generally
usable in most cases.

This solution follows discussion on #70318.

[1] https://github.com/thelounge/thelounge/blob/9ef5c6c67e463c1f401e33b21dfb5641636e5ed1/src/command-line/utils.js#L56