Hi, this is Dr. Gabby. Yes, you are correct in that the eye could dry up. However, you can go to the drug store or walmart and buy "Celluvisc" or lubricating eye drops.
Apply them every 4 hours to the affected eye during the night.
While you are awake I would do it every 2 hours.
If the third eyelid is extended he may have a tiny scratch on his cornea which is the transparent covering of the front of the eye.
So in the morning, he needs to see the vet.
The third eyelid can also extend when the nerves around the ear and the neck are inflamed or injured.
But the scratch on the eye is the most common reason.
The vet will have to put some special dye in the eye to see if there is s scratch. If there is the special yellow dye will stick to the scratch. And then he will be put on an antibiotic eye drop until the scratch heals to prevent infection.
Does that help? Do you have any additional questions?