Whenever you commit a crime, put a +1/+1 counter on Lazav. Then you may exile a card from a graveyard. If a creature card was exiled this way, you may have Lazav become a copy of that card until end of turn. This ability triggers only once each turn. (Targeting opponents, anything they control, and/or cards in their graveyards is a crime.)
Cast cheap interaction and targeted removal/discard to commit crimes each turn, growing Lazav with +1/+1 counters while exiling creatures from graveyards to transform into the biggest, most relevant threat available. You play a controlling Dimir game—answering threats, milling and looting for fuel, and turning your removal into board presence via Lazav's copy ability.
Commits crimes trivially since nearly all Dimir removal, discard, and targeting effects qualify, making the trigger reliable every turn
Doubles as a recurring graveyard-hate engine, exiling key cards while you grow and copy threats
Acts as a flexible threat-and-toolbox: become whatever creature the table has died, from huge beaters to ETB value engines
Cheap three-mana body that snowballs into a real clock while you hold up interaction
Copy effect only lasts until end of turn and triggers once per turn, so it's slow value rather than a permanent advantage
Relies on opponents (or you) filling graveyards with worthwhile creatures to copy
Removal-heavy as a creature; getting Lazav killed in response erases your investment
Lacks built-in evasion or protection, so the +1/+1 counters can be chump-blocked or wiped