When I go to my inventory, it says it's not equipped to my avi. But in actuality, it is. I've tried a lot. (It's the lantern, btw.)
I've tried taking everything off, equipping the item and taking it back off, etc.

What now?

I don't see a lantern on your avi. Perhaps try clearing your cache?

If that doesn't work.. maybe just go to avatar and hit refresh avi.

That should work. Though I think it's just you needing to clear your cache to get rid of it off of your side since I don't see any lantern.