I have spent some time looking at these 3 phase, 3 speed motors generally. They appear to have 3 sets of windings. Two are a Series Delta switchable to Parallel Star like a Dahlander two speed. The third set are wired Star. But I can’t figure out exactly / definitively how they are connected. I’ve found different motor diagrams and lathe switching diagrams but all of them are either lacking information or have inconsistencies For example a unlabelled connection or mismatched terminal designations.
The motor does look to be very inefficient at any voltage or speed.
I’d be looking at a delta connected modern 4 pole motor a with a VFD to attain the speed variation. If the user is more likely to need most power at lower speeds (cutting big bits of tough material) then a 6 pole would be better. You still get the higher speeds but torque would be reduces but OK for small parts or softer materials where yu want high speeds and sharp cutters.