I had a quick look at the switch, it is single phase and think I can see why they wired it direct. This is the switch
This is the back, the red wire should be top right, with this set up as wired you can turn the lathe on, but not off. I had a quick check with the meter and it seems to work contact wise but I won't know if the latching mechanism works until there is power to it. The left hand "on" switch is normally open, and the right hand "off" switch normally closed, if you press the on switch, the current going through the switch should activate the latching mechanism, pressing the off switch break the circuit so the latching mechanism releases the on switch back to normally open. (Incorrect -see edit below)
If it is broken then I will do what I did with my Tom Senior milling machine switch gear. The below was completely broken internally so as I was changing to a VFD, I replaced the innards with a modern NVR switch but the old buttons operate it. I also added the chicken head knob to allow speed control. A new NVR switch would have looked wrong on a 1950's machine.
Tea break over, back to work, it will have to wait until next weekend now
EDIT - the latching mechanism isn't in the above switch, there's more gubbins in the back that I have just uncovered, I thought the switch was a bit small for it's day to be a self contained NVR switch, it is purely a remote controller for the gubbins below, I shall have to look at it in more detail now.
It is looking more likely that I will fit a modern NVR switch to the back of the on/off switch and bypass the existing gubbins unless I can get a decent diagram for it.
EDIT number 2 - found a wiring diagram on the Denford forum
Cheers
Andy