Cats often raise up that third eyelid when they are not feeling well.
As you can't see anything obvious such as eye or nose discharge, sneezing then its going to take some investigation to find out what is wrong.
Make sure your cat has been using the box normally as urinary tract infection can cause a blockage making a cat feel very ill and lack of passing stool can also make a cat feel awful. Make sure no houseplants have been chewed on by the cat as many are toxic to cats and cat at least cause digestive upset.
Here is a quick overview of how I determine if a pet needs urgent care -
If your cat appears dehydrated (see if a pinch of skin over the shoulder blade stays stuck in a tent form or flows back down normally when released), is not eating or drinking, isn't urinating or passing stool, has a rectal temp over 103.5F (normal is 100.5-102.5 Fahrenheit or 38 - 39.2 Celsius ), has gums or tongue that look white, blue, gray or yellow tinted where they are normally pink, has a slow color refill if you press on a pink area of gum or tongue, is having difficulty breathing, or is becoming more lethargic and non responsive to you as time goes on then you may want to get the cat in to see an emergency vet if one is available in your area.
This site may help you locate an emergency vet if you need one
Otherwise you may want to see your vet to have your cat checked over to see what is going on.
There are a number of viral infections, internal parasites, and other health issues that are more of a concern if you cat does go out some of the time.
Hope this helps you!