From the op's perspective it is perhaps worth stepping back to observe that lift as conjectured is that net force which acts in a direction opposite to that of gravity and that arises very simply from the net force over the wing surface. The net force is the sum/integral of the pressure over the surface. When a mass of air is deflected it takes force to do that and that force has to be transmitted as a pressure distribution in the flow. Aerodynamics attempts to reconcile the equations which arbitrate between the fluid and solid elements but newton physics is all you need.