What effect does advising Lily about taking/not taking medicine have on her stats? Does it improve her special, gives her additional armor or something else?
I just find it odd that you don't gain any other perk when you finish her companion quest as the other followers and the medicine bonus doesn't mention what happens to her(excluding the endgame story info change).

I think it only changes her aggression, sanity, and ending slide. You might want to Google or wikia it to be sure.