The other problem with slowing down is also due to the variac.
When you adjust the variac for the speed you want, that is with minimum current (minimum torque, no load).
When you apply a load by trying to lap something, the motor HAS TO slow down somewhat because it has to draw more current to supply the added power. Slowing down reduces the back EMF (voltage) that is opposing current flow, and so allows more current.
When the motor draws more current, the voltage drop due to the variac (which has resistance, etc) increases, lowering the voltage to the motor somewhat. When the voltage is lower, it takes even MORE current for the same power, so the net slowdown is larger than you might expect.
To get around that, a PWM type controller regulates output voltage, which reduces the effect of more current flow.
Some PWM controllers have boost functions which compensate for added voltage drops at slower speeds (lower voltages).
Other PWM controllers can use speed feedback to adjust voltage and current so that the motor speed change is made very small at any speed.
All these effects are made much worse when the motor is made to slow down a LOT, which may be typical of lapping as opposed to straight grinding.