Roger
Last time we had an issue like this it was a dodgy earth.
The mill dro not being affected when you run the lathe at least says the interference is not in the mains.
Try running the VFD through an extension lead plugged into the mill point. If that's still the same then your installation is bad, if it's OK your ring main earth has a break.
My DRO has an external earth point on it, if your does have you used it? I can see a brass screw head? near the mains lead and no earth lead.
The mains lead 'looks like' screened cable, but has holes in the braid big enough to put your head through and will leak like a sieve unless there is also a foil screen we can't see.
The VFD is in a plastic case so no screen.
Terminating the cables via a gland plate has a little known ability to earth all those required cable screens in one go.
In the end you may have to move the VFD further away or buy it a tin box to shut it up