no. humans didn't evolve on their own, they are decended from primate ancestors. primates have eyelids.
see?
other mammals have eyelids too.
in fact, mammals aren't the only animals with eyelids. birds have eyelids
and reptiles (though theirs are different from ours. some reptiles, geckos, for example, don't have eyelids, but rather a clear membrane which protects their eyes.)
and amphibians (theirs are also different, they can't move their eyelids, but instead suck their eyeballs into their heads to allow the two to close.)
as it is, whatever gene codes for an animal's specific variety of eyelid can sometimes be turned off.
cat born without eyelids. magical stuff, this dna.
and here's a page on
eyelids.