It's a well established fact that Lucifer and Alastor do not get along, that should they be left unsupervised for too long one or both will end up bloodied and maimed. So what is Alastor supposed to think when the King keeps seeking him out, that he's not planning to get rid of him? Obviously he needs to prove his importance to the hotel and gain his trust before that can happen.
Unwilling to show any form of weakness, Alastor continues to push himself after the extermination nearly ends him, pain and desperation cutting his fuse shorter than ever. The only one stupid enough to approach him at those times is conveniently the only one he can't fight, but oblivious as the King is, he doesn't catch wise until the Radio Demon nearly crumbles at his feet.
That same obliviousness leaves him blissfully unaware what some of the other residents think is going on.