Lazav copies exactly what was printed on the original card and nothing else, except the characteristics it specifically modifies. It doesn't copy any information about the object the card was before it was put into your graveyard.

Because Lazav isn't entering the battlefield when it becomes a copy of a card, any "When this enters the battlefield" or "This enters the battlefield with" abilities of the copied card won't apply.

Any effects that applied to Lazav before it becomes a copy of another card will continue to apply once it's become a copy. The same is true of any counters that are on Lazav.

If a card in your graveyard has in its mana cost, X is considered to be 0.

If the copied card has an ability that can be activated only once each turn, copying that card a second time will allow you to activate the new instance of that ability.

You perform the actions stated on a card in sequence. For some spells and abilities, you'll surveil last. For others, you'll surveil and then perform other actions.