Okay my 2 cents. If the plane moves with respect to an observer on earth, ie. (plane's velocity) = -(velocity of the belt) with all w.r.t earth, then the plane will have airspeed and therefore lift off. However if the plane is held stationary w.r.t to earth by increasing the speed of the treadmill (very impractical) it is still possible for the plane to take off because the treadmill will push the air too creating a sort of wind tunnel.
Okay my 2 cents. If the plane moves with respect to an observer on earth, ie. (plane's velocity) = -(velocity of the belt) with all w.r.t earth, then the plane will have airspeed and therefore lift off. However if the plane is held stationary w.r.t to earth by increasing the speed of the treadmill (very impractical) it is still possible for the plane to take off because the treadmill will push the air too creating a sort of wind tunnel.