AHC/WI: Lieberman vs. McCain?

IOTL, Joe Lieberman and John McCain are notorious for being extremely moderate for their respective parties. McCain is considered liberal for the Republicans, while Lieberman is considered conservative for the Democrats. Both Lieberman and McCain are rather close friends AFAIK, and I believe that McCain even considered nominating Lieberman for VP. However, how could John McCain and Joe Lieberman run against each other for the presidency? And what would it look like?
 
You could have Gore win and serve two terms. It possible but not likely that Lieberman could get the 2008 nomination. Lieberman is seen as a third Gore term. The Democrats unite behind him. It is 2008 and the President's party loses. .
 
Gore wina 2000 election, dies and Lieberman takes office. McCain vs. Lieberman in 04.

If Gore dies in 9/11, or another terrorist attack, and Liberman takes office in light of that, wouldn't it be more likely he'd keep McCain as his Benton in the Senate for war and congressional dealings? Hell I'd imagine McCain backs Lieberman in a 2004 bid whether or not he gets picked by the Democrats.

To get them driven apart enough to run against each other you'd need a big break. Something like "Jackson killing the Bank" big.
 
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