Parasitic drag has nothing to do with lift. Drag caused by lift is called (lift) induced drag. At high speed induced drag is an almost negligible part of total drag. Unlike parasitic drag which is proportional to the square of the airspeed, for a given lift, induced drag on an airfoil is inversely proportional to the square of the airspeed. In other words if you double the speed the parasitic drag increases four times, while the lift induced drag is reduced to a quarter of what it was.