You'd need a no Iraq War scenario for that. Regardless of what a President Gore would have done Gore was opposed to the way the Bush administration conducted the war-and Lieberman was a major Democratic proponent.
Gore was opposed to what Bush was doing prior to the war so simply having things go better in occupation-(no Bremer etc) is not much of an option there.
Also-at the time Gore endorsed Dean it looked like Dean might be the nominee. His endorsement was therefore in part a reaction to that.
Given the war and the sense that Dean was likely to be the nominee I can't see Gore endorsing Lieberman.