Unfortunately, he has lip licker’s dermatitis.
While it does not indicate anything serious, lip licker's dermatitis can lead to worry. The lips and skin become rough, chapped and can split and even bleed.
Coating the mouth many times each day and before bed at night with an emollient such as Vaseline® or Aquafor® can help. Try not to draw their attention to the lip licking as it usually just causes them to do it more often. If the rash is not responding to the emollients or suddenly spreads or is painful, contact your child’s pediatrician.