It's an interesting debate. I do think Dick Nixon deserves admiration for not contesting 1960, though there are always those who say he just wanted to preserve his hide for a future run.
From Day One, I blasted Gore for not following Nixon's precedent of putting the country ahead of his own victory. But it wouldn't have been illegal for Nixon to contest, and it wasn't illegal for Gore to contest. Just unseemly of a statesman. Things got out of hand with the contest, and some very wrong things were attempted by the Gore side. But I think you exaggerate the degree to which there was a moral mandate for Joe Lieberman to reject the entire 2000 debacle.
It wasn't illegal to contest the results; it was illegal in the way Gore did it. He violated the law in contesting the results, he violated the law in engineering a fixed recount of only Demorat districts, he violated law and decency in attempting to disenfranchised the military.
Lieberman did have a moral mandate to say a) be a statesman like Nixon, b) if the thing must be done, the do it within the law, and c) once laws were broken and scum tactics were used, to speak out against the whole mess.
Not doing so and playing with the team severely diminishes him in my eyes the same way a cheap thug who plays along with criminals because it's easier.