As a senator, Lieberman was often described as a "centrist" (or a "moderate"). But that is a bit misleading. In fact, it is almost akin to Mark Twain's observation that a man with one foot in a bucket of ice water, and the other foot in a bucket of boiling water, "is, on average, comfortable": Mere averages can sometimes misrepresent the truth.
In matters of domestic policy, Lieberman was a fairly typical liberal. But in matters of international policy, he was a staunch conservative. And as Secretary of Defense, he would be involved solely with the latter.
War mongering neocons are NOT "staunch conservatives". It's not 1967 or 1951. The statists are the ones who want perpetual war and empire. And that's exactly what Lieberman is. He's an awful human being.