The actual circuit can vairy from manufacturer to manufacturer, however the usual low pressuresodium ballast is an autotransformer with a capacitor in series wit hthe output. The actual valuse and number of turns depends upon service voltage and the required voltage for the lamp.
You didn't mention if you have a high pressure or low pressure sodium lamp, however the previous description of a ballast would remain the same.
Chances are, when the motor starts, you have a slight voltage sag, either that or the lamp is on one phase of a three phase service and there is considerable unbalance on the service.
Put a chart recorder on the circuit which carrys the lamps load and cycle the motor.
I remain,
The Old Soldering Gunslinger