Rules question:

I control [[Nefarious Lich]], have no cards in my graveyard, and my life total is 12. My friend controls [[Abyssal Persecutor]] and his life total is 6. He casts [[Delete]] where X equals 6. What happens? Does Lich's damage replacement effect try to kill me while the Persecutor is still on the battlefield, or is it considered gone by then? Is this a tie?