I get thirsty with lithium. But I have naturally dry lips... I like uhm... it starts with a B and is more like a medicine. Sorry. Brain not working...

Carmex actually has stuff in it that dries out your lips more (so don't use it!) And I don't know about chap stick.

A lot of meds cause thirst, though. I would ask your pharmacist which ones and they will also have suggestions about what to do.