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One thing the lean does is use gravity to cancel out the torque caused by our feet doing the moving. If you don't lean, you fall backwards because your feet move faster than the rest of your body. It's not so much that we're falling forward and catching ourselves as the lean position is where we need to be for equilibrium.
The angle plays into it, but it's more about the distance ahead of the feet that the centre of mass is to cancel out that torque. Gravity is weaker on the moon, but that also means your foot can't apply as much pressure, so there would be less torque to cancel. Leaning more would further reduce that pressure.
Ultimately, I think the way we'd end up doing it (assuming a more mobile suit or let's say within a pressurized dome) is we'd have to learn to apply less force when trying to sprint/run on the moon. Then we can find an equilibrium that has a similar lean to what we do on earth (and I agree that we didn't evolve for running on the moon and would not be very good at running with a much deeper lean).
This thread is the reason I posted this. So my question is can we calculate the angle you would need to point your shoulders at, and the amount of bounce for optimal speed. (disregarding danger from obstacles and whatnot)
Not a cheetah, maybe more a gazel or kangaroo.