Tame green iguanas do enjoy being handled. They recognize their owners and like being cradled in your arms. Gentle petting and hand feeding are all part of the pleasure of owning these lizards. You should potty train them so they can wander a large room or your house. Many keepers leash-train their iguana while it explores. Just remember to be watchful as these lizards are fast and strong. They are avid climbers and will scale a piece of furniture or a tree in an instant. A leash makes it easier to recover a climbing green iguana.