Does anyone know what Lisa Bonet's reasons were for leaving the show after the first season?

It seems strange that she would leave the show so quickly, considering it was a vehicle built around her.

Also, did she make any apperances on the Cosby Show as Denise afterwards?

Lisa was fired from A Different World by Bill Cosby in 1988 because she was pregnant. Not to mention she posed for playboy magazine. That's what heard anyway.

She made 4 appearances on the Cosby Show after A Different World in 1988. In 1989, she asked Bill Cosby to come back to the show as a regular and he let her come back. In 1991, he let her go because she was losing significance.

She didn't get fired cos she was pregnant. She continuously turned-up late for filming and some days she didn't even bother turning up at all. She was bound to get fired cos of that - when she ended up pregnant the producers must've just thought that was the last straw and she got chucked.
Also, Bill Cosby wasn't too pleased about Lisa's role in Alan Parker's "Angel Heart" in which she appeared alongside Mickey Rourke. Cosby actually asked Parker to cut one of the scenes from the movie but the director refused.