One could reasonably assume that in The Company of Myself, Kathryn is Jack's lover. In Fixation, they seem less like lovers and more like really good friends. This likely has something to do with the fact that Every Point Of View Is Different.
There is also the fact that all we have to go on regarding the notion that Jack murdered Kathryn is the word of what seems to be an unskilled psychiatrist. It's possible that she died in an accident and, panicking/grief-stricken/maddened, Jack did something irrational that made the police think that he'd killed her. The events in-game actually mirror this idea, though the events in Fixation make it possible that he killed her under the influence of his medication. We may never learn the truth.
Fridge Logic: The psychiatrist has met Jack every week for the past eight years, and every time Jack says the same things, including asking him not to leave. It gives me the impression that if the shrink had stayed, Jack might have reached an epiphany, and he never will now. This obviously wasn't what the writers were going for.
It's noted that, on some reviews, the reviewer notes that a shrink would have recognized Korsakoff's Syndrome, or at the very least, anterograde amnesia. The author not being a psychologist, it's acceptable, not to mention that, while Jack is obviously in a fantasy world, it's highly possible that he doesn't remember the psychologist due to his "travels". You try meeting some guy once a year, have a chat, and he leaves, then you roam about the world and meet again. Chances are, you wouldn't remember him without some prodding.
More on topic, you'd think they would hold more psychological appointments, even if Jack was really violent.
They meet once a week.
In TCOM, it is mentioned that Jack has, apart from the therapist appointments, remained in solitary confinement. There's pretty much nothing that will mess up a person - even one who is relatively stable - like solitary confinement, and in modern times, with awareness of this issue, only extremely dangerous (including to themselves) patients are held in solitary.