Copying with Lazav does not make Lazav enter as the copy, he is still on the battlefield, still the same permanent, he just looks different. So the Sovereign doesn't trigger at all.
However, you could get Lazav to copy something in response to the Sovereign's trigger, when he enters (possible with either Lazav). Then the token will enter as a copy of whatever Lazav is copying at the time the trigger resolves, complete with all modifications to the copy process. If Lazav is copying Phage, the token's controller will suffer from her "lose the game" trigger, since the token wasn't cast from the hand, it wasn't cast at all.