This explanation/demonstration made it clear for me.
I was under the premise that the treadmill would equal the speed of the aircraft, thus there would be no forward movement and no air to flow over the wings in order to generate lift (i.e. OP scenario #1).
This demonstration shows that the treadmill will never equal the speed of the aircraft. Therefore, the aircraft will always be able to move forward and generate the lift needed for flight.
I was blind, but now I see LMAO!!!