Where was the lizard caught (country, state, etc)? There are deserts all over the world each with its own fauna so you need to be more specific.
Tell us more about its appearance.
Try crickets for food. Most lizards want to eat something that moves. Also, throw in a dandelion, clover flower or piece of green vegetation in case it's an omnivorous or herbivorous lizard.
Make sure the lizard is warm for 12 hours a day by setting up a heat lamp to produce a 90-100F warm spot. Just a spot, not the whole cage. Spray some water into one area once a day.
As soon as someone can identify the lizard, more specific care can be addressed.