The last few tokes you take of a blunt or joint. The burn gets low enough to cause a small yet alarming amount of pain to the smokers lips. Thus was born, burnt lip.
Ryan: "Wow, this blunt is great, you want burnt lip?"
When someone fucks the lips of a vagina so hard that the forskin of the penis becomes red and soar in a stinging manner. (Basically feels like a sunburn)