What evidence suggests that limbless bodies are the result of convergent evolution of snakes and lizards?

The evidence that suggests that limbless bodies are the result of convergent evolution of snakes and lizards is the fact that snakes and lizards with limbless bodies evolved from different ancestors of legged lizards.
Convergent evolution is the process by which unrelated or distantly related organisms evolve similar body forms, coloration, organs, and adaptations.  Another example of convergent evolution is the similar nature of the flight wings of insects, birds, pterosaurs, and bats. They all serve the same function and are in structure, but each evolved independently.