The most important lesson of the Iraq War, I think, has been that an overconfidence in military power has been replaced by an understanding that there are severe limitations on what can be achieved by military means.
Intervening swiftly with arms and crippling strikes might be easy for a great power, but achieving desired political aims is another matter and exiting may be hard -- the phrase "If you break it, you own it" comes to mind. Vietnam, Afghanistan and Iraq have been long and costly engagements with very mixed results. Since then prudence has held the U.S. back in the case of Libya and so far in Syria.
Another important lesson is that today armed international interventions are likely to be condemned by much of the world unless they are clearly in self-defense or have been authorized by the Security Council.
Iraq was neither. Unless we remember this going forward, I fear there is nothing stopping this kind of tragedy from being repeated.