First of all, VP isn’t president. Also, Lieberman had been a Democrat for most of his career, except the very end when he turned Independent, so maybe there was some dumb Democratic idea that this would bring him back to the fold.

In any case, it didn’t work, and they lost the race, in part because many Democratic voters weren’t thrilled with Lieberman, whom many saw as a turncoat for leaving the Dems and going independent. So choosing an independent certainly didn’t inspire the Dems to ignore their rules in the future.