The majority of geckos lack eyelids. They have a transparent membrane over their eyes that keeps them moist and offers a certain amount of protection, but they still need a way to clean them off every so often. Above: A demonstration of the way they clean them off every so often.
Some species, like Lialis burtonis, have additional adaptations that let them keep their eyes out of harm’s way.
The exception to the “geckos don’t have eyelids” rule would be the family Eublepharidae, which has about thirty species, lacks sticky toe-pads, and seems to like hanging out in deserts.
Of course, just because they can do this:
does not necessarily mean that they don’t also do this: