I had a question- if I'm making homebrew content for a game that uses LUMEN and includes the "Illuminated by LUMEN" license/image, do I need to include the LUMEN license text/image or should the one in the main game be good enough?

You should add the text and image to your thing as well.

Gotcha, thanks for the response. Minor follow-up; would this apply to any "lore/fluff-only" homebrew as well, or is it just for "mechanical" supplements?