The reactive force to this acceleration of air downwards is additional lift
There is no "additional lift". Best think of a propeller, it's just an airfoil that gets its airspeed by rotating, the pressure difference between the forward and rear faces causes the airflow to flow in a rearwards direction at considerable speed at the beginning of take off, so providing thrust (lift as far as the airfoil is concerned).
Force(thrust or lift) = mass X acceleration
= d(mV)/dt
where d/dt = derivative with respect to time eg rate of change with time, mV = momentum, product of mass and velocity
Lift is often explained as throwing air at the ground, stand beneath a hovering helicopter for an example, or behind a stationary prop driven fixed wing running at high power.