You pivot the front wheel to turn, the leaning is secondary. It's to counter centrifugal force so you don't fall over.
Edit: I'm mistaken and didn't account for camber thrust which happens when "a point on the outer surface of a leaned and rotating tire, that would normally follow a path that is elliptical when projected onto the ground, is forced to follow a straight path while coming in contact with the ground, due to friction. This deviation towards the direction of the lean causes a deformation in the tire tread and carcass that is transmitted to the vehicle as a force in the direction of the lean." https://en.wikipedia.org/wiki/Camber_thrust