There are myths related to low pressure (such as the infamous "equal transit time" theory), but low pressure generating lift is not one of them.

The pressure explanations and the Newton's Third Law explanations are not different theories of lift. They are just different ways of looking at the same thing underlying thing.

The motion of a wing through a fluid has to conserve mass, energy, and momentum. If you analyze lift by focusing on conservation of momentum, you get the Newton's Third viewpoint. If you analyze by focusing on conservation of energy, you get a pressure viewpoint.

See: https://www.grc.nasa.gov/www/K-12/airplane/bernnew.html