Can you pick up a lizard?

Yes, you can pick lizards up. However, if you have a lizard that hasn't been handled by people very much, it may be frightened by being picked up. With practice, they will learn that being picked up is ok for them.

Lizards should always be gently lifted from underneath with your hands supporting their bellies, and never by their tail. Their tail will probably break off as a defensive tactic, and very few lizards will regrow their tail if if breaks off.