Hi I had a dragon egg in the front of my base on the Zombie server. It was 6 blocks away from my open entrance. Since I am pretty sure that someone took the time to lag into my protected region and click the dragon egg to make it move, is that punishable?

nope, griefing is allowed on zombie server.

but it was a protected region, yesterday a mod said it was not allowed to take from a protected region so yeah

Griefing allowed = protected zone or not, its allowed.

if you plan to place an egg, best make sure it is somewhere where no one can get to even with lag. there is no way to really tell who touches it to make it move