How does smoking affect your lips?

Badly. Smoking affects "lip lines" in two ways: 1. The repetitive movement around the lips as a result of puckering repetitvely can lead to vertical lines around the mouth. 2. More importantly, smoking can lead to elastic fiber and collagen degeneration in the skin, which as a result, can lead to sagging and wrinkling of the perioral skin.
Dries and ages them. The lips are basically composed of the same tissue as the rest of your skin, at least on the surface, and smoking's effects on reducing skin elasticity and causing premature aging and wrinkling are seen in the lips as well. There also may be darkening of the lips. There is every reason to stop smoking, even just for your ego and to look and feel better. Stopping will help u live longer/healthier.