NASA has a webpage on aeronautics that says lift is the mechanical force created by a solid object turning a flow of liquid or gas. They also have an equation for calculating lift for any solid object/fluid combo.

The wing experiment with hundreds of pressure sensors shows lower pressure on top and more on bottom.

It is known yeah. Another user commented it. If you take a wing and put it in a wind tunnel you can put sensors in its wake to measure the pressure. By manipulating the fluid flow you can change the pressure. So low pressure on top and high pressure on bottom. Multiply that by the surface area and you get a force. Smaller force on top of the wing, lower force on the bottom of the wing. So the wing goes up. Of course theres some physics going on in the fluid that explains the change in pressure, but this is just a quick and simply-put explanation because I took a fat amount of zquil and am tired.

Source: Im getting a PhD in aerospace engineering

Edit: I had to do this in a wind tunnel during one of my undergrad courses. It was fun playing with the wind tunnels, would recommend