I did not understand why Lotterman hated Moburg so much (I never read the book).
In my opinion, Lotterman treated Moburg like he'd been a jilted lover - (Like Moburg dumped him).
Also I cannot understand why Moburg wasn't just paid and fired? (Or not paid but fired)
Lotterman didn't like Moburg in the book because he was crazy and hard to control. Yeamon, who isn't in the film is a young hothead who threatens Lotterman but initially refuses to fire him because he'd have to pay him one month's severance. In the end he fires Y. but refuses to pay him a cent. I guess it would've been a similar case with Moburg.
The journalists in the novel don't spend much time at the office so as long as they were producing copy to put in the papers, I guess Lotterman didn't care too much. Moburg also takes a beating from the unionist protestors outside the office at one point and maybe Lotterman saw him as some form of security. If they're brawling with M. at least they're not beating the others.
In the film Moburg is a mixture of Moburg in the book plus Zimmburger, a half-crazy ex-marine who lives upstairs from Sanderson, and also some of Yeamon. Lotterman is a hack and teetering on the edge of manic depression so it's hard to say what his motivations always were. He was under a lot of stress running a paper in that environment without the proper motivations.