I know that work = force x distance
The key that you may be missing is that it's force x distance
in the direction of the force.
In the case of lift, there is no movement in the direction of the lift, so no work is done.
In the case of drag, the aircraft moves in direction of the thrust, and therefore work is done by the thrust (against the drag). It's immaterial that the forces balance, you still do work when you move in the direction of the force.