I had the benefit of watching this movie while babysitting for my neighbors. Apparently despite being clearly designed off of a green iguana, he's referred to as a tuatara. I know it's a kid's movie that isn't meant to be taken seriously as science, but that greatly bothered me (even more than when the turtle is able to lift his shell without removing his spinal cord)
I think it's neither an iguana or a tuatara. Leo is clearly designed exactly like an iguana, including a lot of them being invasive in Florida in the movie. But his 'species' lives to be over 100, they have inflatable throat sacks, can change colour and have the typical frog/chameleon tongue.
They're a typical mixed bag of lizard types that we can see in a kid's movie