Several things can cause burning lips. You might have an allergy. Your lips are sensitive to the sun so you may have a sunburn. If they burn in the winter, it could be windburn from the cold air. Maybe you chew your lips and don't know it. Drinking drinks that are too hot can make them burn.
The actual cause of burning lips are still unknown. Burning lips usually associated with diseases like menopause, psychological disorder, hormonal imbalances, etc.