Stanford Children's Health states that to heal a split lip, the wound needs to be washed daily, kept dry and treated with ice to help with swelling. Once the cut has healed over, sunscreen can be applied each day to minimize scarring.
When dealing with a cut on the lip, stopping the bleeding should be the first objective. Pressure needs to be applied to the wound until the bleeding stops. If the bleeding does not stop after 10 minutes of applied pressure, medical attention should be sought. Once the bleeding has stopped, cold water can be run over the split to clean the cut. Antiseptic creams can help reduce the risk of infection, and ice or cold compresses can help minimize swelling.
A cut that occurs near the outline of the lips may require stitches even if it is small. The stitches are not necessarily for closing the cut; rather, they are required to keep the outline of the lips even and smooth.