That's an Anolis of some kind. I'm guessing it's a green anole (Anolis carolinensis) or maybe the brown anole (Anolis sagrei).

Are you keeping it warm and well lit? It should have a basking spot of around 90F and some additional bright lighting. I use incandescent lights in a clamp-on dome light for heat and a small fluorescent fixture for additional lighting. Also some humidity. Spray the enclosure a couple times a day. It will like to lick up the drops of water. It looks like it has plenty of artificial plants to crawl on and hide under. Keep the lights and heat on about 12 hours a day. Don't let the temperature drop below around 65F at night. Keep it away from cold, drafty places and heat vents. Also if it's in a glass enclosure don't place the enclosure in the sun. Could heat up excessively and kill the animal.

If it's warm it might eat. But it may also be slowing down because it's autumn. From the photos it looks healthy.