I know this is a little old but thought I would chime in. There are a number of things that leopard geckos are very prone to getting that can cause the eye to close.

-Usually a stuck shed is what it is but the eye will look swollen or bulging if it was.
-if it is in sand or any of kind of dirt particles of some sort could have gotten inside and havnt came out.
-There are a few worm parasites that are found around the eyethat can cause them to close there eyes.
-If it was scratched lets say by a mealworm while trying to eat it, could cause them to close there eyes.
-Nutritional deficiencies as well can cause this, usually lack of vitamen A.
-Some geckos are born blind (not in this case apparently)

Usually the best thing that you can do is try to flush out the eye with a sayline solution that they use for contacts that is preservative free. If that doesnt help a vet trip is needed.