There is a pressure difference with an asymmetric airfoil, and that results in air being directed downward with a resulting upward reaction force. F=ma still holds, the lift force is equal to the mass × acceleration of the air downwards, likewise momentum is conserved as the momentum of the plane up equals that of the air going down.

All of the lift can be explained by Newton's laws, but explaining why the air moves down in the first place can't be explained by Newton's laws.