Leaning and turning are independent in the case of an uncoordinated turn, but this only occurs during transitions in lean angle or perhaps a pothole dodge maneuver (described below). Uncoordinated turns are only temporary, eventually a bike will fall inwards or outwards in an uncoordinated turn.
The key point I'm making in my answer is that the linear component of this is the same regardless if the bike is falling or not. Centripetal acceleration is equal to the centripetal force exerted by the pavement on to the contact patches of the tires divided by the mass of bike and rider (force = mass x acceleration, so acceleration = force / mass), regardless if the bike is leaned properly or not (falling inwards or outwards).
The purpose of leaning properly is to keep the bike from falling inwards or outwards during a turn.
In a coordinated turn, the bike needs to lean inwards enough so that the outwards torque related to inwards centripetal force at the tire contact patches and the outwards reaction force at the center of mass is exactly countered by the inwards torque related to gravity pulling down at the center of mass and the pavement pushing up at the contact patches.
In an uncoordinated turn, such as dodging around a pot hole, a bike can be quickly turned to get the tires out from under the bike to go around the pothole, but the bike ends up leaning the "wrong" way, and this lean has to be corrected for after passing by the pothole.
More common cases of uncoordinated turns occur during transitions in lean angle during corner entry or corner exit.
In case the OP is asking how lean angle effects steering inputs, I'm adding this geometrical explanation in this part of my answer.
In a steady turn, the path of a bike is a circle, and the radius is from the path of bike to the center of the circle. 544
Ignoring factors such as tire deformation or slippage, the radius is a function of steering angle and lean angle.
In the imaginary case where a bike was vertical and not leaned, the center of the circle would be where the imaginary extension of the front and rear axles intercept. In the case where a bike is leaned over, the intercept point is below the pavement, and the center of the circle would be a point on the pavement directly above the intercept point below the pavement, and the circle and radius would be smaller. I'm thinking that the effect of lean angle probably multiplies what would be the "vertical" radius by the cosine of the lean angle. So if leaned at 45 degrees, the radius is cos(45) ~= 70.7% of the "vertical" lean angle radius.
Note that this doesn't have anything to do with balancing of the bike, it's just the geometrical combined effect of steer and lean angles. 544