is there a way to Lock a pet as a further precaution to not get it zapped or changed?

/The regular zapper can "zap items unlocked" in your inventory, change your pet into a strange new species or destroy the minion it has attached/

There are no REs or anything that have a negative affect on your pets. You have to select a specific pet for the zapper to zap, and it will only zap the pet you've picked. So there's not a way to lock pets out of being zapped, you just have to be careful to make sure you click on the pet that you actually want to zap.