Re: 240 volt motor, switch, reversing switch questions
Normally I'm firmly in the camp of not using standard lighting switches in motor applications, but I have a slightly different take on this one. Your 4way is just altering current paths and not breaking the circuit while under load, so as long as you don't accidentally flip the state of that switch, you should be fine. "Should" is the key word in the last sentence. Obviously a drum switch is the best choice, but again, as long as you power down the motor, and IMO get the lathe to a full stop beforehand the 4way will be fine.
Now without specs, it's impossible to say whether or not the start/stop station can handle the motor load. However, you have to manually change the state of yours, whether on or off, so it leads me to believe that it was not designed for low voltage applications where typically the buttons are momentary in nature. So while I can't say for certain that it will do what you hope to, I can say I'd use it in a heart beat if I were you.