There is no neutral on the machine. It has 3-phase and ground. The transformer is connected between the two leads from the utility company, not the generated leg.
The instructions for the DRO say “It is recommended that the unit’s case is grounded to the machine. Use a wire … from the cabinet equipotential terminal (refer to manual) to a suitable point on the machine body.
Damn Brits, wish they would speak English. Worse than Thermite.
So before I hook ground to the machine, I thought that it might be necessary to tie primary and secondary circuits, so that the ground actually has a relationship to the secondary circuit.
Definitely try grounding it.
Beyond that, you are dealing with electrical noise. Electrical noise is a bit of a black art. Even amongst electrical engineers. But basic principles aren't too complicated. The general approach is 1) find the source of the noise, 2) find the path of the noise to the problematic location (DRO). 3) Mitigate either 1) or 2).
DROs use a high gain amp on the wires to the scales. This is the noise sensitive part of the DRO that will result in a flickering display, if everything else is behaving.
Noise can get into the DRO via any wire, as any wire acts as an antenna to some extent. Or it can come in through other things connected to the power source. Power supply wires, or scale wires. Scale wires are normally inside a metallic sheath of some sort, which acts as a shield to keep noise out of those wires. And there is no other electronics connected to the scale wires, so nothing else there to create noise. So in your case the power line wires are suspect. The fact that the transformer output floats does increase the noise sensitivity, as there is not a low impedance high frequency path to ground through the transformer. In other words, floating makes it a better antenna. But it does not cause the noise.
I understand that the lathe is powered via 3-phase w/o 120V. I would assume you have 120V somewhere in the building. I'd connect the DRO to 120V with the lathe otherwise powered off first, to be sure that the problem goes away. Hack up and extension cord or whatever. Just to confirm assumptions that electrical noise from the lathe's internal guts is the issue, diagnostic only.
Then with the same extension cord/hack in use, turn the lathe on and see if the problem occurs or doesn't occur. If it does occur, you rule out the transformer as the path of noise. If it doesn't, then the transformer is part of the noise path, although very unlikely the source.
You could even go as far as disconnecting the wires from the transformer output and splicing that to the extension cord as a 2nd step to test the noise source and path.
That's the systematic way to proceed. The shotgun approach is to put some ferrite beads/choke on the power supply line going into the DRO to try to reduce suspect noise.