That’s what your basic mistake is. You’re assuming the plane will not create any lift. I was thinking the same thing until I stopped to think about it. It will, just as much as normally. The treadmill does not affect the normal operation of the airplane in the slightest. Plane ignores treadmill, speeds down treadmill/runway odd contraption, since it doesn’t use shaftwork transmitted to wheels, but thrust, and it generates lift as it normally would, and takes off as it normally would.