Buffer
All I can add to your description is if the workshop is detached from the house and the earthing in your workshop is connected to the PME house system the conductor needs to be a minimum of 16mm.
Sometimes with a detached workshop earthing is provided by an earth stake with a RCCB controlling all circuits, in this case any cpc/earth conductor (inc SWA) in the supply cable is insulated from the workshop system.
It may be a good idea to get the earthing arrangement with the inverter and supply to the lathe checked by your electrician for peace of mind at least.
Emgee