Well, Zack saw Lyta as a person and not a telepath, but it's hard to be buddies with someone that can read your thoughts.
I think it's hard for us, here watching a tv show, to appreciate the difficulty of having to deal with a real telepath being someone you see in life. And these characters are really written to be like a person, ( they seem to have thoughts and feelings that aren't dictated by the plot of the week but their own "life" experiences) so that's got to be creepy on some level no matter how much you like someone.
Plus, they really were broke at the time.
It's nice to say, "couldn't they let her stay there" but the amount of revenue that room could bring in could keep them from having some problems. No free lunch, indeed. It's a fact that a lot of real world people have a major problem accepting so it seems doubly so on a show where tv people always have what they need unless the plot calls for it and even then they get through the plot and still have it in time for the credits, usually.
Plus, I'm not sure Sheridan forgave her for blowing up Za'ha'dum.
And she was a buddy of the Vorlons, which in some ways makes the Corps look not too bad. I mean the Corps have guys like Bester, but the Vorlons are the Vorlons. And after Kosh died, most of the Vorlons mercy toward the younger races did, as well.