I know this may be a contrary view but I really don't care if Lieberman continues to run or not.
I say let him run and lose.
Connecticut is not a state where there is any realistic chance of a Republican winning the election because Lieberman is splitting the Democratic vote, so what's really the harm except that we will have to spend some money and energy campaigning. But the benefit of a strong Lamont campaign will be a strong turnout that will help in the three congressional races in which Democratic challengers are now rated toss ups against Republican incumbents.
Realistically, the only argument that will sway Lieberman to consider dropping his campaign will be polls showing that he has no chance of winning. If we reach that point that he has no chance of winning that what is the harm in his running and losing ?