Alistair trying to fight Adam only proves that he has a deal with Lilith. Since like we see once Adam is dead Lute tells Lilith in heaven to go see her daughter Charlie because of a deal between the two. Alistair was trying to bring Lilith to him by killing Adam. He failed but it still worked out as Lucifer weaked Adam and Nifty killed him. Between his deal with Charlie and him trying to kill Adam. Alistair was getting ready for Lilith to return. So whatever deal he made with her can be over. Now granted their might be a small hole in this theory. As at the end of episode 8 Alistair is trying to find a loophole in his deal. Why would he need a loophole if he has a deal with Charlie and because of Adams death Lilith would be coming to hell. I can't answer that but I think this theory is really solid. Just have to wait for season 2.