Unfortunately it does not sound good for the little one. As its problems are congenital and not trauma or disease induced, I suspect nothing short of an x-ray and blood workups is going to reveal the problems. Given that it has a deficient external organ (the non-functioning eye), internal deformities or lack of proper organ function/s is a very real possibility. Diagnosis would not be cheap and there is no guarantee the issues are treatable or can be managed.
In the meantime, I can only suggest trying a wider variety of food items to try entice it to eat, if it can. Good quality canned cat food is very high in protein and helpful in putting condition on thin individuals. (It should not be used a staple but only an occasional treat in healthy animals, for the same reasons.) Mixing it with chopped up snail or slug might make it more appealing. You might also try small woodies (feeder roaches) or chopped up larger ones, as they are also very nutritious. Most small insects or spiders etc. can also be offered. Flies with their wings removed and fly maggots fed on bran, pollard or powered milk for a couple of days, are also good, being slow moving and nutrient rich. You might also try small earthworms or chopped up larger ones.
Using a plastic teaspoon, so it doesn’t feel too cold, try placing a little a the food item on the lizard’s lips so that the next time it pokes its tongue out it gets the taste of it. If likes it, it will lick off what remains on its lips. If it doesn’t, it will either ignore it or try to wipe its mouth on the substrate. If you get a positive reaction, then offer a little more. Do this a couple more times so that it can recognise the taste and smell, and it should then feed itself when that food is provided.