This is kind of like trying to count the horse's teeth while sitting at the kitchen table.
The only real way to get a good answer that will serve your immediate need is to have a qualified electrician witness the dimming lights and do some tests. The causes are varied. Some are benign, some are malign. . .so, because of the latter, don't put this off.
The benign cause is voltage drop caused by the resistance in the wires that supply the power and a change in current on those wires caused by the motor start currents, and the human eye's peripheral vision sensing this fluctuation of light.
The potentially disasterous cause is a failing, maybe burning, connection, or an open neutral.
Impossible to tell from here.
