The basics
The overall strategy of this deck is very much in line with Wheel decks, though has some key differences. While some table wheels are included (e.g. Windfall, Jace's Archivist), the deck is far more focused on self-wheeling and discard/draw than say a Nekusar, the Mindrazer style of deck which is aiming to machine gun the whole table through wheels. Cards like Tolarian Winds then take the place of Ill-Gotten Gains or Dark Deal. Focusing on self-wheeling and discarding gives the opponents much less opportunity to draw into a response, and rather helps us focus on getting as many draw/discard/cycle triggers as possible to benefit from.
Lazav and Friends
Lazav, the Multifarious allows us to sink colorless mana into his activated ability to shapeshift into a creature in our graveyard at instant speed. Lazav then begs for things going into our graveyard - it's why he has Surveil 1 on entering the battlefield, and why most EDHrec pages look like Surveil tribal with some bigger cards like Entomb or Buried Alive to get that oh-so-predictable Vector Asp + Phyrexian Dreadnought combo. Cycling, however, allows us to pitch creatures (and other cards) into our graveyard while simultaneously replacing themselves with other cards.
Now, I know what you're thinking. Creatures with cycling typically aren't that powerful, and you're not wrong. This isn't all that bad however, as many cycling creatures don't generate nearly as much threat. For your opponents, cycling a Horror of the Broken Lands into your graveyard simply looks like you are pitching a bad card (even for pauper standards) in search for something better. This contrasts heavily with using an Entomb on a Phyrexian Dreadnought, or Eater of Days or Leveler which draws attention and telegraphs the strategy pretty blatantly. These kind of Lazav decks become a race against graveyard hate, which Lazav can handle fairly well due to his aggressive cost, but ultimately, makes the strategy fairly linear. Cycling doesn't draw nearly as much attention in filling your graveyard as using an Entomb or Buried Alive and has the added bonus of replacing cards lost and help search for answers. Finally, many of the cards that cycle can also benefit from other cycling effects. Cycling Horror of the Broken Lands gets you a card while pitching itself to the graveyard, and benefits from future cycling events. Activating Lazav's ability to become the Horror can become deadly with wheels or a cycling engine online.
Lazav Targets: Cycling, Discarding, and Drawing triggers
Lazav has a number of targets at his disposal for different purposes, but many of which benefit from cycling, discard, and draw triggers.
For evasion and protection (asides from equipment like Whispersilk Cloak), Lazav has: Invisible Stalker, Dimir Infiltrator, Cunning Survivor, Dirge of Dread, Wasteland Scorpion
For beats and voltron, Lazav has: Horror of the Broken Lands, Cunning Survivor, Grisly Survivor, Shadowstorm Vizier, Toothy, Imaginary Friend, Chasm Skulker, Vile Manifestation
For control, Lazav has: Archfiend of Ifnir, Ruthless Sniper, Wasteland Scorpion
As well as a host of other creatures (e.g. Psychosis Crawler, enchantments (e.g. Faith of the Devoted), and spells (e.g. Tolarian Winds, Decree of Pain) to help him along the way!
Sequencing and Lazav
Given that Lazav's activated ability costs , we can activate it at instant speed and relatively easily given that there is no mana-fixing constraint. Understanding how to sequence Lazav's ability thus becomes crucial, as you often need to layer his activation with a specific order in mind to get the most out of any given situation. Activating Lazav's ability to become a creature with evasion FIRST is crucial in order to get through the blockers step. An example would be to move to combat, activate Lazav's ability to become an Invisible Stalker, a Dimir Infiltrator or perhaps something with flying like Shadowstorm Vizier, then declare attacks. Opponents cannot block, which then opens up for followup activation(s) of Lazav's ability before the damage step, say transforming to a Horror of the Broken Lands. This then allows for cycling in order to pump Lazav (Horror of the Broken Lands) to get in for good damage.
Having Training Grounds out in play immensely helps with this, so that we are more easily able to transition between creatures when needed, and sink mana elsewhere (e.g. Faith of the Devoted, Drake Haven, etc.). In some cases, we can simply swap between 2CMC creatures without any trouble - in one game I was able to swap to Invisible Stalker to give him evasion and hexproof, swing in, and after blocks but before combat damage, swap to a Vile Manifestation for free, and use my mana to cycle as many cards as I could and get in for a Voltron win. This is also crucial for protection, as when Lazav gets targeted with removal, you can swap to Invisible Stalker with Training Grounds out, even if you are tapped out.
It's also crucial to keep in mind that while Lazav copies other creatures and gains their abilities, he retains his name. This means that Commander Damage, even if done with a mix of Lazav copied as a Horror of the Broken Lands and a Chasm Skulker will ultimately be tied to Lazav. The same holds for +1+1 counters, which is why Toothy, Imaginary Friend and Chasm Skulker are included here. Both benefit from draw triggers, which this deck has a lot of potential for with cycling, in the form of +1+1 counters. Both are then fantastic value engines as you can play them directly from hand, hopefully get a few +1+1 counters on them, and if they die, so be it - you just drew more cards in the case of Toothy or a got some squids in the case of the Skulker. Now that they are in the graveyard, Lazav can copy them, and start to get +1+1 counters on draw triggers, but if Lazav changes to another creature he gets to keep the +1+1 counters. This means that sequencing and weaving activations of Lazav when you know you will draw cards is crucial in order to consistently pump him up. This can be as simple as activating before your upkeep if one of them is in the graveyard and you have some extra mana in order to get at least one more +1+1 counter by main phase, or doing so before you know you wheel or cycle-storm in order to net batches of +1+1 counters.