Lazav, the Multifarious

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.

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.