Sort of. (And caveat: I'm a software guy, I just happen to love airplanes.)
Airplanes generate only forward thrust (unless you're in a VTOL craft which we won't talk about). This forward force is what ends up generating lift due mainly to two particular, but separate, applications of physics.
First, wings take advantage of what is called Bernoulli's principle. Picture a wing: it is longer on top than it is on bottom due to the "chamber" of the wing. I.e., the asymmetric difference in the shape of the top and bottom of the wing. This causes the air that flows over the wing on top to be at a different speed than the air on bottom, since the air on top gets compressed. (Remember that in a river, if the river narrows, the current speeds up because you still have a stable amount of water to get downstream. If the volume status the same, higher pressure = higher speed, roughly.)
So, by Bernoulli's principle, the slower air on bottom has more potential energy than the air on top -- and that results in more outward pressure by the air, i.e., it pushes up on the wing harder than the air on top pushes down (which has more kinetic energy and less potential, due to the higher speed). Because the wing is not creating energy, the air is merely converting to and from kinetic/potential.
However, that's not the entire story of lift!
Wings are also angled, with their trailing edge down as compared to the leading edge. This angle is defined as the "angle of attack". Think about it like this: when you stick your hand out of the window of your car while driving down the freeway at high speed, you can tilt your hand up and "take off". The wind hitting your hand pushes it up because of the angle. This seems kind of straightforward, right?
If you continue tilting your hand closer and closer to the vertical, at some point it falls back down. You have "stalled" and are no longer generating enough lift to fly. Airplanes do the same thing, so they have to balance the lift they generate with the other factors.
Airplanes fly mainly through the combination of these two things: lift generated by the relative difference in airspeed above and below the wing, plus lift generated by the angle of attack.
I hope that is explanatory, and if I'm wrong on anything, someone else will come correct me!
Your picture of how lift works is fairly off base.
The speed difference being due to asymmetry is wrong. Symmetric wings still generate lift by having air flow over the top faster than the bottom. Symmetric wings flying upside down also still generate lift that way. Asymmetry helps, but is not necessary.
The important thing to understand about aerodynamic lift, and that few people do understand, is that the Bernoulli's principle action and the air deflection action are the same thing. They are not two different mechanisms which act in concert. They are two different ways of looking at a single phenomenon.
If you deflect air downwards, you will generate a speed and pressure differential between the top and bottom of your wing. The pressure differential will produce an upward force on the wing that is precisely equal to the downward force on the air. Likewise, if you generate a pressure differential between the top and bottom of the wing, you will deflect air downwards. They're two different results of the same action.
To truly understand why wings generate lift (which is the same thing as why wings generate a faster airflow over the top than the bottom, or why wings generate a lower pressure on top than on the bottom, or why wings deflect air downwards), you need to understand the Kutta condition.
A wing moving through air has two stagnation points, which where the airflow splits. There's a stagnation point at the front of the wing. Any air above that point goes over the top, and any air below that point goes underneath. At the back of the wing, the stagnation point is the point where the air from the top and bottom meet again.
The location of the front stagnation point depends on the angle of attack. If the wing is flat, the front stagnation point will be right at the leading edge. As you tilt the wing upwards, the front stagnation point moves toward the underside of the wing.
The Kutta condition says, in short, that air won't go around a sharp corner. Thus, the rear stagnation point is always at the trailing edge of the wing. This is why wings are shaped like a teardrop, and that sharp edge at the back keeps the rear stagnation point from moving around.
With the front stagnation point mobile, and the rear stagnation point fixed, you have an asymmetry that causes circulation. This is a rotational component to the airflow around the wing which causes air to flow over the top faster than the bottom, such that the stagnation point is at the trailing edge. This circulation causes the air to be deflected downward, and causes lift.
In summary, wings generate lift by deflecting air downwards, which is equivalent to saying they generate a pressure difference between top and bottom, which is equivalent to saying they generate a speed difference between top and bottom. Wings accomplish this by having a sharp trailing edge, which causes circulation that deflects the air. Wings are shaped the way they are not because the asymmetry is necessary to generate lift, but merely because it's more efficient that way, by changing where the front stagnation point occurs, or by generating less turbulence in the air.
Airplanes generate only forward thrust (unless you're in a VTOL craft which we won't talk about). This forward force is what ends up generating lift due mainly to two particular, but separate, applications of physics.
First, wings take advantage of what is called Bernoulli's principle. Picture a wing: it is longer on top than it is on bottom due to the "chamber" of the wing. I.e., the asymmetric difference in the shape of the top and bottom of the wing. This causes the air that flows over the wing on top to be at a different speed than the air on bottom, since the air on top gets compressed. (Remember that in a river, if the river narrows, the current speeds up because you still have a stable amount of water to get downstream. If the volume status the same, higher pressure = higher speed, roughly.)
So, by Bernoulli's principle, the slower air on bottom has more potential energy than the air on top -- and that results in more outward pressure by the air, i.e., it pushes up on the wing harder than the air on top pushes down (which has more kinetic energy and less potential, due to the higher speed). Because the wing is not creating energy, the air is merely converting to and from kinetic/potential.
However, that's not the entire story of lift!
Wings are also angled, with their trailing edge down as compared to the leading edge. This angle is defined as the "angle of attack". Think about it like this: when you stick your hand out of the window of your car while driving down the freeway at high speed, you can tilt your hand up and "take off". The wind hitting your hand pushes it up because of the angle. This seems kind of straightforward, right?
If you continue tilting your hand closer and closer to the vertical, at some point it falls back down. You have "stalled" and are no longer generating enough lift to fly. Airplanes do the same thing, so they have to balance the lift they generate with the other factors.
Airplanes fly mainly through the combination of these two things: lift generated by the relative difference in airspeed above and below the wing, plus lift generated by the angle of attack.
I hope that is explanatory, and if I'm wrong on anything, someone else will come correct me!