He was trying to distance himself from Bill Clinton as much as possible. Remember, Clinton was still quite unpopular at least on a personal level c. 2000 (despite the public viewing his overall tenure in office -particular on the economy - quite favorably). And IIRC, Lieberman had been one of Clinton's harshest intraparty critics during the Lewinsky scandal era.
Keep in mind, though, that running mates didn't usually make much of a difference to election performance even back then (and to a greater extent than one might think, that's still true).
Conservatives didn't need to attack Lieberman, though; rather, they could simply attack Gore instead.
Maybe, but the thing is that Graham would have delivered Florida for Gore. Indeed, couldn't some people have already predicted back before November 2000 that Florida could decide the outcome of the 2000 U.S. Presidential election?
