The Liberal Party's endorsement had more to do with the close relationship between Giuliani and the party's leader, Raymond Harding, than any sort of liberal ideology on Giuliani's part.

Raymond Harding's son, Russell Harding, was one of the most corrupt members of the entire Giuliani Administration.  Bernie Kerik couldn't hold a candle to that guy, frankly.  The fact that Raymond Harding gave Giuliani an endorsement in exchange for letting Harding's son rip off the city is an interesting piece of NYC history, but let's not try to draw any electoral implications from it.