May be lip eczema. Persistent dry or chapped skin near or on the lips may be lip eczema, which can be treated like skin eczema, using Hydrocortisone cream for a week, plus vaseline or aquaphor to retain moisture. Lip sunscreen chemicals sometimes can cause an allergic reaction on lips. Other times, a person is a primary lip-licker (it is a habit). Once cracked, lips get irritated by routine foods, juices, & saliva.
Depends. Perioral dermatitis can be allergic, infectious, fungal, or just irritative. The treatment, therefore, depends on the cause. Cracked, dry lips (especially at the angles) can often be helped with vaseline alone. Allergic or irritative can usually be treated with a short course of steroid cream. If red, blistered, draining, or crusting, you should see a doctor for recommendations.