Put pressure on a cut lip to stop the bleeding according to the University of Rochester Medical Center. Wash the cut area with soap and water, but do not scrub the wound. Dirt left in the wound during healing causes scaring at the site of injury.
Apply an antiseptic lotion to the cut, notes the University of Rochester Medical Center. Keep the area clean and dry, and apply sunscreen with a sun protection factor of 15 or higher to the wound to prevent scarring. Call a health care provider if the wound is deep, long, the result of a puncture from a dirty or rusty object, contains debris, the result of an animal or human bite or shows signs of infection like redness and swelling.