Regard this one as a comment
I prefer to cite some text form this website instead of providing the link only (as it could be removed).
In general, this pattern can be observed across the planet with the
size of lips and nose decreasing as we move away from the equator
towards the poles. So what could the reason be?
For someone living in hot climatic conditions, cooling down the body
is critical for their survival. Our body has many cooling mechanisms
and one of them is simply disseminating heat when it comes in contact
with colder air (simple thermodynamics). This however requires larger
surface area so that more heat can be disseminated.
Given that a significant portion of breathing also happens through the
mouth (especially when exposed to heat), lips are pretty much like the
gateway for colder air being inhaled and exhaled. So, the larger the
lips, the more heat that can be disseminated. Thus, people living in
hotter climatic conditions gradually evolved to have bigger lips.
The opposite is true for people in colder climates. They get a
survival advantage if they are able to retain as much heat as possible
and so they gradually evolved to have smaller lips thus limiting the
amount of heat that can escape when cold air brushes past their lips
while inhaling and exhaling.
Notably, there was no scientific source provided for this claim, however intuitively this could make sense.