[Remi warned him about this. Might as well be as clear as humanly possible.]

If you mean kill, no. I didn't even find out the old man was Lucifer since he took on a few different forms. Plus he was just a spectator, not the real threat.

And if you mean debt, I don't owe him anything. He wanted to see me fight, and even made me fight against every Fiend he had, including the four horsemen and Beelzebub. He offered me a position as a general and more power but I declined, thanks to the future Dante.