I have seen this type before, and it ended up causing the leo to die, i do not know what it is, all i can say is go to vet and dont let it near other leos, it may be contagious

Is it a baby? I had this happen to 4 babies that I bred myself, they were the last 4 to hatch, only the last one survived because she did not lose her appetite. For the eyes, I would soak them and put terramyacin (spelling?) in their eyes, you can get that at a vet. I would have to reopen their eyes every few hours and reapply the terramyacin. For their mouths, I would put either a tiny bit of hydrogen peroxide or betadine on a qtip and rub it on the corners of their mouths. Unfortunately, 3 of them stopped eating and became very thin and weak and I eventually put them to sleep. The 4th one I would hand feed mealworms and small crickets to and she would always eat at least one or two and that kept her healthy but definitely not fat. Their mouth crusties cleared up pretty fast, it seemed to be the eyes that were the last straw. 

Like I said, the only reason I didnt give up on the last one is because she kept eating, and finally, one day, her eyes just stopped swelling and sealing shut, now she is totally fine, her pupils seem to be a bit off, but no worries, and she is TINY for a year and a half old, but now she eats like a champ and is gaining weight fast. Her name is Rah, you can see her in my animals :)

So, if your leo is still eating, dont give up yet! If it is really weak and listless and thin, putting them down at a vet might be the better option.

Hope this helped. Oh, and I kept all of my babies in separate containers so I would not know if it was contagious. I would separate them just to be safe.

Sounds like a bacteria or virus. Quarentine the animal, give it assisted feeding so it doesn't deplete the gecko of energy and you're going to have to take it in if it's swelling and not eating. This is not a simple cure. If you have swelling of the eyes and discharge you need medical attention.

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