I have heard of this happening, but I dont remember ever seeing it. It happens usually when there is some stored energy in the appliance, e.g. capacitor or in this case a slowing motor which is in effect a generator and a single pole switch or a double pole switch where the poles are not switched at the same time. It can also be caused by arcing in the switch confusing the RCD.
It is difficult to diagnose as there may also be a normal earth leakage current on the RCD circuit from other appliances which is putting the RCD near to its tripping point allowing a small additional earth leakage to trip it. If any appliance have been added to the circuit this may explain why it did not happen in the past.
I would start by checking the RCD to see what the normal earth leakage is on the circuit and that the RCD is functioning at the correct leakage current. Then turn to the lathe switch possibly substituting an alternative as a check or try turning it off at the wall switch to see if the lathe switch is causing the problem. Also worth checking the start/run capacitor to make sure it is ok but if there were a problem with this or the motor I would suspect the fault could appear at turn on.
Just in case you are not aware of how an RCD operates: it measures the imbalance between the Live and Neutral conductors and if it exceeds a certain amount it will trip the circuit on the assumption that the imbalance is a leakage is to earth and therefore a fault. A 30mA RCD will normally trip between 20 and 30mA and should not trip at less than 15mA. So even though the live has been switched off in a single pole switch a current flowing in the neutral will exceeding the RCD trip value trip the RCD.
