M.P.
I suggest this is related to his ADHD and a processing disorder that frequently goes along with ADHD,but not his medicine unless the one he's taking causes his mouth to be dry. My grandson licks and sucks on his lips and frequently has a red chapped ring around his lips even when he's not on medication.
He's in special ed and they encourage him to chew gum. Sucking on hard candy would also help. Sucking on a straw to drink water might also help. The told us to have my grandson suck and blow on a straw for occupational therapy. He's had chapped lips less often since starting this.