What if the justification remained a lie, but the occupation created an Iraq that was a functioning liberal democracy?

War never creates functioning societies; only dysfunctional ones.

Being Devil's Advocate here (obviously), but I'm talking about the occupation (which wasn't entirely clear) and it's severely destabilizing effect and boosting of anti-american sentiment in the region and, by extension, boosting of Islamic Extremism

If an Iraqi liberal democracy had been created, I have no idea what it would look like. It's very hard to imagine, as that region has a very weak history of democracy. However, we could probably predict that it would end up looking something like Turkey's system, with Islam being much more present in government. It's likely that the power struggles between Sunni and Shia Muslims would be represented in a parliament or house of representatives (whatever legislative assembly they create), and would, as in our timeline, be greatly inflamed by the American invasion.

The occupation of Postwar Germany formed a functioning (and extremely successful) democracy in a country that had very little history of democracy. Might there have been a more Belgium/Bosnia style arrangement?