Hi, to clarify, the motor in your link can use the variable speed knob as an actual speed control on a lathe, as-is? Or does that speed knob set the "max" rpm of the motor, and you still need to rig the foot control to another potentiometer to use on a lathe?
The first of these i bought maybe 6 or 8 years ago is the type linked by Tommy-D.
Procured, wait for it....to replace the clutch motor on my wife's Consew.

Just now i went up, slipped the belt off (so as not to create a snarled skein of thread without sewing anything), and ran the motor through its paces to verify my memory:
You can hold the lever down (on) and dial with the dial from 0 to max rpm.
Alternately, the dial can be set for max rpm, and the foot pedal used to control (vary) speed. More or less.
Both work fine & are positive, but they are not fine tuning.
If i intended to use in-process variable foot pedal speed control, i'd arrange the leverage so it took a fairly large travel to fine tune the short travel of the lever. If you just want to lock it -on- and vary rpm with the knob, it will work fine.
I have one each, of 2, slightly different kinds of the programmable "brushless servo motors". One is mounted on the rotating center set used on my planer for cue tapering and turning. You can set ("program") the max rpm, and use the lever for a foot pedal if desired. Same notes about abruptness as above. I've never seen a need for the foot pedal, so removed the spring (default is off with spring) and set the lever by hand.
Also have one on 4' x 4' x 8' convection oven i'm building for thermoforming plastics, to run the impellor. That will be on or off, to a pre-set speed. Not sure yet what speed will be optimal for uniform heating without a lot of excess tempest going on.
So the brush type has 2 options for in process control.
The brushless type, max speed is set by "programming"; if you want variable, the lever has to be used.
Brushless type also increments in 100 rpm steps only.
Both types seem solid and stable to me, perhaps the brush type is a little more, how shall we say, "elegant". Like a bimmer to the chevies. But that does not imply i have a preference.
Caveat - it's possible they might change specs of these units over time, this is a report on the ones i have, most recent (3rd) received & installed last week.