It's worth noting that the diagram you've shown is a common misconception; it's almost identical to the one on this NASA webpage explaining what's known as the "transit time" myth. In fact, it's the exact image given under the "Misconceptions" section of the Wikipedia page on the Bernoulli principle.
In short, the myth states that because the upper surface is longer, air must travel faster to cross it in the same time, and thanks to Bernoulli's principle we know that air travelling faster is at lower pressure, and this low pressure therefore exerts a force that draws the wing upward.
This is actually wrong twice. Firstly, there is no particular reason why the air travelling over the top surface should have to take the same time as the air going underneath; indeed, it's pretty simple to put a wing in a wind tunnel and release a puff of smoke ahead of it, watch the smoke puff split into two pieces at the wing's leading edge, and observe as those pieces reach the trailing edge at different times.
Secondly, this gets the cause and effect of Bernoulli's principle backwards. If you apply Bernoulli's equation to the wing-in-airflow scenario, you can actually show mathematically that the air flowing over the top surface of the wing must take less time than the air passing underneath.
Either way, the explanation is actually much simpler. In your diagram, the airflow somehow returns to being perfectly horizontal behind the wing. In reality, air that strikes the wing horizontally at the leading edge ends up leaving the trailing edge with some downward velocity (and again, you can derive this mathematically from conservation of momentum). For the air to have gained downward velocity, it must have been acted on by a net downward force. If the wing has imparted some downward force on the airflow, then we know from Newton's Third Law that the airflow must be exerting an upward force on the wing.
It's true that there are pressure effects caused by the change in effective cross-section area of the various airflows, and these do affect the wing's ability to exert that downward force, but by and large the lift force can be explained in terms of momentum and Newton's Laws.