Re. "gains from lift".
Oops. So far as I know, the act of creating lift by aero effects by necessity demands power from the system and does not give any benefit, unless you're trying to get off the ground to fly.
Actual weight reduction helps of course - because the engine now has less mass to accelerate. Merely reducing the force of the wheels against the ground by lift (or by a whole bunch of helium balloons) does not reduce the car's mass. So the engine's job is not easier.
Of course it takes energy to lift part of the car's weight off the ground, which ultimately comes from your engine and your fuel. From what I've read here before, that penalty occurs as drag. All other things being equal, a car with more lift will have a higher drag coefficient. Nuttin' comes from nuttin', and NSTAAFL: no such thing as a free lunch.
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Coast long and prosper.
Driving '00 Honda Insight, acquired Feb 2016.
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