I had the same issue. Thought it was because I stopped taking anti-histamines, but yesterday I stopped eating salt and it vanished.
Could that be the cause of your peeling lips?
UPDATE : I reject what I said. Salt doesn't change my lips. I'm thinking it might be stress or something else... Though my lips are quite okay atm. When I put sangre de grado on them they immediately become soft. Still searching for the cause...
