He is possibly having a kind of eczema
that is known as Lip Licker's Dermatitis
. This has occurred due to frequent licking and irritation and dryness of surrounding skin due to saliva.
To treat the same, apply Vaseline over lips and surrounding areas along with application of mild steroid
cream like fluticasone
cream twice in a day. Also ask your child to stop licking his lips and peri oral area.
Hope that solves your query. Take care.