Biden
I really don't think many people are sick enough to put in a Democratic President and a Republican Vice President (and vice versa). It would be a disaster and there really isn't a partisan advantage to it.
Unless the Republicans do the unimaginable and gain a Senate seat this election, there is no way a tie results in a Republican Vice President regardless of what Lieberman does in this hypothetical. The way the rule is written, it takes 51 Senators, not 50 plus the Vice President to settle the tie. (Nor would a vote of 50-49 settle the issue.)
