There is lots of good advice here, but ultimately it’s all too vague and laden with platitudes to be of much use. Yet even at that general level, some of these “lessons” deserve to be questioned. The idea that counter-terrorism needs to take a back seat to stabilization sets up a false dichotomy. It is hard if not impossible to achieve any stability without minimal security. A key to counterterrorist operations is enlisting support from the local population, giving them the stability to return to some version of normalcy and to hope and plan for a better future.
The lessons from Iraq are many, but one is not to go in without a plan to win the peace or to declare mission accomplished prematurely. Another is not to withdraw too soon or we will watch whatever we have built collapse in sectarian struggle. Above all we need to never underestimate the determination and skill of the forces opposing us. They are not a JV team. They have been fighting for centuries before we got there.
Finally we must be wary of what we are trying to stabilize. Starting with Iraq, many of the nation states established in the region after WWI are inherently unstable. Across Lebanon, Syria, Iraq, and Iran, last lines need to be redrawn, new more homogeneous states crested, plebiscites held and populations transferred to arrive at a more stable state structure. There might be a Kurdish state in parts of Iraq, Iran, Syria, and Turkey. There might be two Shia-Alawite majority states, two different Sunni Arab states, and even a Christian state. Stability is unachievable in and of itself. A diplomatic vision comes first.