The law of the lever says that "the less force you use, the more distance you have". It is often exemplified by referring to simple machines, but it should apply to all technical systems. But I do not see that airfoils comply with this principle.
For example, an airplane in steady, level flight that has a lift-to-drag ratio of 20 has to invest 1 N of thrust to obtain 20 N of lift. So the input force is amplified by 20 without having a longer distance to go.
Maybe one can say that no work is done just by holding the airplane up in the air, so the law of the lever cannot reasonably be applied. But the same principle holds true when the airplane starts to climb using lift. In a steady climbing maneuver the airplane gets additional potential energy but has to invest only 1/20 of the force of what would "normally" be required when it would use no lift. Since the thrust only has to be big enough to overcome the drag and not to overcome the weight, the engine can be less powerful, which equals to less chemical energy consumed over time.
I haven't done a rigorous calculation yet, but I am almost sure that an airplane with a very high lift-to-drag ratio gains more potential energy in a climb than what is consumed in chemical energy to produce thrust. That contradicts the law of conservation of energy of course, but I am a skeptic of that principle.
What do you think? Am I on the wrong track?
