When a gas flows over an object, or when an object moves through a gas, the molecules of the gas are free to move about the object.
Because the molecules move, there is a velocity associated with the gas.
Within the gas, the velocity at different places near the object have different values.
Bernoulli's equation relates the local velocity to the pressure in a gas; so as the velocity increases the pressure must decrease. Adding up the pressure variation times the area around the body determines an aerodynamic force on the body.
According to Newton's third low, a turning action of the flow will result a re-action (aerodynamic force) on the object. The integrated velocity variation around the object produces a net turning of the gas flow. Adding up the velocity variation around the object also determines an aerodynamic force on the body.
Integrating the effects of either the pressure or the velocity determines the total aerodynamic force on an object.
Lift is a component of this aerodynamic force.