For minor chapped lips, vasoline will do the trick. If your lips are severly chapped and the skin is splitting, this could promote infection. Check with a doctor.
First, you need to get some good chap-stick. Medicated chap stick might burn a little and it isn't really for sunburned lips. I recommend some with aloe. Secondly, stay out of the sun and wash around your mouth with cool water since warm or hot will cause worse burning sensation.
Use a moisturizing chap-stick as needed, Carmex generally works best. After you've healed, apply carmex every other night before bed, to help prevent chapping. It does burn, but works wonders!