That sounds like stuck shed. They can get pieces of shed stuck up under their eyelids. You have to be careful because that can cause infections and infections often lead to pus build-up around the eyes. Since pus in leopard geckos is hard, it has to be surgically removed.
I'd suggest soaking the gecko every day for about 20 minutes in lukewarm water to try and loosen the shed. Your friend can try taking a q-tip wet with sterile water and gently running it over the stuck shed to get it off, but under no circumstances poke the gecko in the eye and don't be rough, be very very gentle.
It's also a good idea to add some vitamin A to the diet. It can help with both eye issues and shedding in general.