The eyelash thing is part of the larger phenomena of cuteness. Mammals, be them human babies or puppies, have larger eyes in relation to their heads. It's one of the things that identifies them as young. Women use makeup to draw attention to their eyes, to make them appear bigger and therefore more youthful. So while men may have thicker eyelashes, it is women who generally accentuate their eyelashes, resulting in the social convention that any cartoon with drawn eyelashes is female.

Look at the animation in Archer. Lana and Archer both have thick eyebrows, but Archer doesn't have any eyelashes.