Hi,Thanks for query,
Many a time you have habit of moving your tongue on the lip very often will result wetness and then dryness of the lip leading to cut on the lip.
Quit this habit if you have.
Apply moisturizing cream or Vaseline on the lips.
Do not pill off the dry skin
as this will lead to bring infection and infected cut.
Take B. complex,Iron and multivitamin
Keep oral hygiene
Ok and bye.