Hi Dick, This is my first post here but I actually sell Motor Speed Control Packages on eBay for purposes like this. As per all the other comments, you will need to use a three phase motor that is operated by a single phase input drive. This is because single phase AC motors can not operate with variable speed while maintaining torque.
The drives I use with my packages are made by AC Tech, I've uploaded a pdf of the manual
here, if you wish to read up on it. These drives will operate a motor from 0 to 240 Hz. For example, if you had a 1800 RPM 60 Hz motor, you could run from speeds of 0 to 7200 RPM. However, constant torque will only be maintained when running the motor above a ratio of 30:1 of the rated motor speed. At lower end speeds the motor can also get extremely hot, so if you plan on maintaining a slow speed for more then 5 minutes, other cooling may be necessary. You even program acceleration and deceleration times into the drive, as well as up to 3 preset speeds. Everything is controlled by the buttons on the face plate but the drive has terminals where you can attach a forward/reverse, start/stop, and speed up/down switches. Also available is a remote keypad that has buttons for all of these as well as a digital readout.
If you have any questions or concerns, please feel free to reply to this thread or email me and I'll be more then happy to help. I can even put together a motor package specifically for your lathe if you can provide me with spec information about your lathe motor and the kind of power/voltages you have available in your location.
-Koko Ratanaphasouk
Friesen Electric
eBay Store