Good Morning K.. I would think you could use a chap stick on your little guy. I use them on our gr. son's that I keep daily. Don't use anything with menthol in it though as that burns. There is one that is like a gel in a small tube, I have used before. If you have some vaseline you could try a dab of that on his little lips.
Right now I have a tube of Blistex for the boys.
Laughing I made the mistake once of picking up a red or pink tube of chap stick. Guess what It was tinted. Corbin had red lips...lol
I have no idea what causes it so much, Corbin licks his lips a lot and they get chapped. Sometimes if their little mouths keep milk on them while sleeping they can get chapped.
Hope someone has better advice for you K..
God Bless you and your precious little Miracle Man.
K. Nana of 5