It is not a race thing. I have read that straight, overhanging noses evolved as an adaptation to cold climates, but I can't remember anything about lips. I think there is a general trend for some races to have smaller or larger lips than others, but obviously, as with most genetic traits, there is a large range of types in each population and race. Therefore, it is likely that fuller lips are the original human state. Large lips may have arisen by natural or sexual selection.
Lips are a very sensuous part of the body and look attractive.
The disadvantage wouldn't necessarily have to be large to change the genetic makeup of a population over many, many years. I think this is less likely. As an artist, though, I am able to see and appreciate the differences and beauty in everyone I run across. It's a good question. Blacks come from a hot climate.