Rearrange and get:

CL(AoA) = Az.m/(q.A)

(Az = vertical acceleration.) The relationship between coefficient of lift and AoA is a known function that depends on the airfoil. As long as you're below the critical angle of attack, it's an invertible function. (If you're not below the critical AoA, you've already departed controlled flight so it's too late for MCAS.)

> In flight, the lift is nearly always equal to the weightlab times load factor. (From your link)

This is not true at or near stall conditions.

How so? As far as I understand, it will hold to a very high degree as long as the flight conditions are stable over the time scale needed to establish the airflow pattern over the wing, which is very short.

(If the flight conditions are that unstable, a mechanical AoA vane will struggle too, since it has mechanical inertia.)