I'll be honest....I did not really watch this show on NBC, but I've begun to
enjoy it in reruns on Nick at Nite.

On "Cheers" Fraiser (Kelsey Grammer) is married to Lilith (Bebe Neuworth.
They have a child and live as a married couple.

I know Bebe Neuworth made several guest appearances on "Fraiser" but she
was not a regular as she was on "Cheers." How was she written out of
"Fraiser." Did Lilith and Fraiser divorce?

Basically at some point during the last season, Rebecca sees Lilith with another guy and tells Fraiser. Few episodes later, Lilith tells Frashier that she wants to spend a year apart from him living in a Biosphere (with her new lover). Few episodes after that, Fraiser receives word that Lilith wants a divorce.

I'm not sure what you mean by "written out". Lilith was always a secondary character. I believe Cheers ran a while before her first appearance.

But yes, they are divorced. She sometimes appears on Frasier when visiting or when his son visits.

As for a reason, I'm trying to remember if this was a topic on Cheers. Any one recall?

[edited to add:]
Oh yeah!! The Biosphere! That was funny. Didn't she run off with one of the crew?

Yeah, I remember her coming back from the biosphere. I think Bebe Neuwirth (sp?) wanted to some play or something, and that was the way they gave her time off.

But I also remember her returning and saying that she wanted to give it another try with Frasier, and by the end of the episode, he agreed. And then they got back together, didn't they?

If I'm correct, anyone know what happened between that episode and the beginning of "Frasier", when Frasier and Lilith are clearly divorced?

You're remembering correctly except for the "got back together" part. There was an episode where she returns from the Biosphere and they discuss giving it another shot, but ultimately decide not to. They were still divorced when Cheers ended its run.

Not to go too off topic, but weren't the charactes of Niles and Martin Crane completely invented for "Frasier?" I don't think eithe a father or a brother were ever mentioned on Cheers.

In fact, I think Frasier mentions that his father is deceased (and not a cop) in an episode of Cheers.

Its a spin-off... They have to add characters and such, even if they talk about them being dead and such. Whatever happened to the brother in Hapy Days, Chuck?

Yes, but they actually "fix" this in one of the episodes of Frasier... I think it was the one that Ted Danson guest starred on. Frasier introduces Sam to his dad and sam says "You said he was dead". Frasier tells his dad that he was "angry with him at the time" or something like that.

I never saw that one, but I remember a previous discussion about it that had the dialogue, something like:

Martin: "why did you tell them I was a scientist?"
Frasier: "Well what did it matter? You were dead!"

Wish I could see that one.