How long wil it take broken skin or a cut on your lip to heal?

Usually a few days.: Unless chronically irritated, chewed, or reinjured, small lip cuts heal within a few days. Keep a small dab of Bacitracin on it to keep it moist and protected (and it keeps you from licking or chewing it--tastes bad). If it doesn't heal or comes back, you might be dealing with something else--have it checked out by a dermatologist.