This is Cricket-Catcher, in case you haven't met him before. He is a Cuban Knight Anole and he is a Predator. See his teeth? You don't want to be an earthworm in our yard – your days could be numbered.
Bill was trimming the plants in the lizard's tank, and Alex wanted to pet the lizard, so Bill got the washcloth and used that as a barrier between him and Cricket-Catcher's mouth when he lifted him out of the tank. The lizard latched on to the washcloth and wouldn't let go, so Bill switched hands and held the lizard with one and the washcloth with the other.
See that flap of skin hanging down? He trots that out – it's called a dewlap – when he needs to appear ferocious. He also turns a slightly darker shade of green.
But Alex got to pet him, and I think Julia did, too, and after that, Cricket-Catcher went back into his tank, let go of the washcloth, and probably spent some quality time cussing out the annoying humans who are only good for bringing him delicacies from the back yard.