I think this is a simple tactic, but one that bear fruit. Much like republicans refer to the Democratic party as the "democrat" party, all of our discussions should refer to Lieberman as "Lamont's Republican Opponent". Hopefully Lamont would only refer to Lieberman as "My Republican Opponent" on the stump.
Why? As LBJ said, make the bastard deny it. If Joe asks why he is being referring to that way, the answer is "Look who endorsed you, do you reject their endorsements?" If he embraces the endorsement, it becomes Lamont against Bush. If he rejects the endorsement and label (enough and emphatically) Republicans may ask why they are supporting him.
Here's to the defeat of Lamont's Republican Opponent!