Sounds more like chapped lips gotten out of hand. This remedy is cheap and it works. Purchase BLISTEX in a tube and place a small amount on the index finger. Work the cream on both lips and all around the lips. do this at least hourly. You will be surprised how soon healing takes place.
It can be due to dermatitis skin or perioral dermatitis. Treatment consists of oral antibiotics and anti-inflammatory drugs. A mild soap or soap substitute, such as Dove or Cetaphil should be used for washing. Scrubbing should be avoided. He should avoid licking the lips as saliva evaporates quickly resulting in them being drier than before. Make him drink plenty of water. Use a humidifier to moisturize the air in your home and apply shea butter or Vaseline on his lips.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your dermatologist. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.