What is there to do about a cut on your lip?

Moisture : Most minor lip cuts will heal relatively quickly but vaseline will moisturize the area and speed healing. If it is more deep or significant, then you may need to see md for sutures

First aid: Much like a cut anywhere else on the body, you should seek to clean it of debris if any is present. Use mild soap/water or hydrogen peroxide. Once cleaned, you want to protect the area while it heals and keep it moisturized. If it crosses the border of the lip onto the skin above/below, see a doc with experience in facial repairs to prevent adverse healing.