According to HowStuffWorks, a couple of home remedies to easily treat a minor burn include the application of honey, cool water, or if the skin is not broken, an ice cube. If using an ice cube, rinse it under water first, so it does not stick to the lip.
HowStuffWorks also suggests the use of vinegar and water mixed in equal parts; this solution works as an antiseptic. Another remedy, which is soothing, is to apply a milk-soaked cloth to the lip, repeating every few hours. It is important to wash after each use or the milk will sour.
For minor burns on unbroken skin, MedlinePlus advises rinsing with cool water and then applying a clean, cool wet towel. Once the lip area is dry, it should be covered with a sterile bandage. If pain persists, ibuprofen or acetaminophen can alleviate pain and swelling.
MedlinePlus also notes that minor or first-degree burns affect only the outer skin layer and cause pain, redness and swelling, while second-degree burns affect the outer and an underlying layer of the skin, causing pain, redness, swelling and blistering of the skin. When third-degree burns afflict the skin, they cause white or blackened charring and possible numbness.