A friend suggested it but personally I think Lazav fits a better purpose and is more versatile.
It could definitely be added to the Zombie Build. For the moment I've been working closer with the Main Build but it's definitely in the realm of possibility since I did find a slot for it in the Main Build.
Since the ability you're using is on the Necrotic Ooze and not on Lazav per se, you don't get the bonus from Embalmer's Tools. It would have to be of a creature card in the graveyard, like Genesis. Since the creature activating the ability isn't in the graveyard (although Necrotic Ooze is copying the ability of a creature in the graveyard) it doesn't get the bonus. At least that's what I'm concluding.