The basic lift equation (F=MA) can be re-written a little bit using the Kutta-Zhukovsky theorem,

Lift = airspeed * circulation * density * span

Energy is really the primary component of lift. The ground effect shifts this energy to a smaller alpha value, because of the things explained in the previous thread.

It is really tough to explain circulation dynamics properly in a small amount of time...

Basically any vortex carries momentum. This is what produces lift: the motion of the wing converts some upwashing air into some downwashing air. This results in an increase in the downward momentum of the air, and imparts upward momentum to the airplane. Momentum per unit time is force, and this is the force that supports the weight of the airplane.

The ground effect gives the aircraft less induced drag [and lessening the 'power required' (for the reasons in the previous thread)] this gives more energy at first (which is responsible for the initial increase in CL)... however the energy from the vortex is missing, giving a loss in lift - which contributes to CLmax forming at a lower alpha. The reduction in lift induced drag is what gives the CL shift to the left (per alpha). This doesn't truly increase the total lift.

If you look at the table for alpha/CL values in Aerodynamics for Naval Aviators - you'll see that total lift is never increased (a total shift to the top per alpha with an increase in CLmax), rather net lift is increased at a specific alpha, but total lift remains the same or even less in some cases.