Lieberman probably helped in this part of the world, especially among Jews, although Gore paid dearly for that pick elsewhere. Although Gore was reticent to tie himself too strongly to Clinton, there was much goodwill from that administration in the region (see the 92-96 swings in these states) that seems to have held over enough for Gore to pull off surprising wins in Bush-Bush-Clinton counties like Monmouth, NJ, and Richmond, NY.
Gore did not "pay dearly" for having Lieberman on the ticket. He was an asset at the time who nearly helped Gore win Florida.
Or he could've just gone with Bob Graham to actually secure Florida.