TC,
Before you lower the lever, both sides are in equilbrium, with the total rotor thrust acting through the C of G in all planes. So the transverse distribution of thrust is balanced. If you lower the lever, the only thing that changes in your lift formula is CL as you say. If the CL changes by the same amount around the disk, then wouldn't the distribution of lift remain the same? (Yes it would). Since you are not changing V, if you halve the CL on one side, you halve it on the other. So if CL changes by the same amount around the disk, there would be no flap back/forward. Remember that the relationship between AoA and CL is not linear and the CL around the disk will be distributed differently after the lever is lowered. So there will be some form of flapping, but the extent and direction of flapping would depend on the airflow regime and the blade design.
When one lowers the lever, the total rotor thrust is reduced, thereby reducing the horizontal component. There is an imbalance between this and parasite drag causing a pitch forward couple. Also, as the aircraft starts to descend, the AoA of the horizontal stabiliser decreases, reducing the downward component of the force acting on the tail, causing a tail up couple. I am sure there are other more subtle effects as well.