I like the way you build this deck. Perheps I will build a similar Lazav deck. Thanks for the inspiration.

Foil would probably be a decent replacment of Force of Will if you are still looking for a free counter. Nyxathid could also be a nice addition to this deck.

Thanks for the suggestions!

The problem with Foil is that it rips two cards from your hand. In a deck that doesn't have many ways to produce "clean" card advantage (apart from Phyrexian Arena and Rhystic Study), this can be a remarkable drawback. I still think that Misdirection and Pact of Negation are more preferable, but I do see its potential.

As for Nyxathid, I included it in my initial build of the deck. Being a 7/7 is very important because it represents a 3-turn clock, but apart from that there aren't many other reasons to want it in the deck. It doesn't have evasion nor trample and it costs three mana to copy, which makes Phyrexian Dreadnought, Hunted Horror and Eater of Days strictly better. I can see it as your "plan D", but I don't think you need it that bad. You can consistently get the three aforementioned creatures whenever you like, so I would not include any other.

Have you considered running Monastery Siege instead of Search for Azcanta?

I honestly think it's even better for when you have a card in hand that you want to discard, but you don't have a discard outlet available. when you're in this situation it essentially draws you 2 card, and lets you discard something you either don't need, or something you want in your graveyard.

Monastery Siege is a card that I was considering when I was building the deck from scratch. I do agree with you that drawing and then discarding is significantly better than the surveil 1 of Search for Azcanta  ^Flip.

There is, however, a big issue that kept me from including the Siege in the deck. The Khans ability is mandatory, it's not a may. With the enchantment on the table, you will have to loot every turn. This won't be a problem in the early game, when you will have plenty of cards to discard. In the mid to late game, however, when you will have fewer and fewer cards in hand (this deck doesn't generate too much card advantage, since we are mainly looting) and your creatures will already be in the graveyard, choosing a card to dump will be painful. Imagine a situation where you have two counterspells, a removal spell and a land in hand. Generally speaking you want as much mana as possible to activate Lazav more than once each turn, so the land won't be an easy discard. This means that you will have to get rid of a spell, and that's a real pity because they are very useful. On top of that, this unpleasant situation will happen again every subsequent turn that you have the Siege on the field. Overall, I think that the enchantment will end up doing more harm than good.

Search for Azcanta  ^Flip is less explosive, but much more efficient in the long term. We can sculpt the top of our deck for our first turns of the game, and once the enchantment flips we have an extra land that can help us dig some extra cards to find the answers we need.

A cool suggestion indeed. The only problem is that it will be very hard to catch an opponent off guard with it since it will be in plain sight in your graveyard. If they see you have a Phyrexian Obliterator in the bin, they simply won't attack into you. If you want to use it offensively, they won't block. For this reason, it can be seen as ": give Lazav unblockable". This is a little too expensive, especially if we compare that to our other evasion tools (Invisible Stalker, Dimir Infiltrator, Looter il-Kor, Key to the City). If you want an element of surprise, you need an instant-speed way of putting the Obliterator into the graveyard (Entomb, Key to the City), and this seems a little too clunky in terms of mana management for a one-time blow-out. My deck tries to be as mana-efficient as possible, but I can see the Obliterator included in other lists that have a bigger focus on cool combat tricks.