Lieberman probably helped somewhat in New York, New Jersey, and his home state, but those three states were never going to be hotly contested, and he more than made up for it with the damage done in the rest of the nation.
Lieberman probably also helped Gore in Florida among Jewish voters and Northeastern transplants in Palm Beach, Broward, and Miami-Dade, contributing to that state's extreme closeness. But he was a net liability to Gore elsewhere, causing him to lose many votes to Nader, and hence explaining why states such as Oregon and Minnesota were so close that year.
Would Bob Graham have been the best choice? Stop the bleeding else where but also helps in Florida
Graham may have helped in Florida but having an all-southern ticket could have hurt him elsewhere. I think Shaheen would have been the best pick would have helped him in NH and the Northern states but probably turned off fewer leftists than Lieberman did.
Gore's campaign made several key mistakes though he shouldn't have distanced himself from Clinton. Clinton's personal favoriblitiy was low but people were happy with his economic policies.