The most popular motor for the cutting lathes is a Technics SP02 direct drive motor which is quartz locked for speed accuracy and weighs ~110lbs with plenty of torque.I doubt this statement. It implies that there are more lathes using the Technics motor (which is great) than those that don't. The simple fact is all lathes unless custom built are vintage machines. Mine is typical- its a Scully built about 1948 or so, equipped with a Westerex cutterhead and electronics from about 1970 (refurbished). The lathe portion didn't see much change over the decades until Scully ceased production altogether- the big change was how the cutter head was advanced across the LP (IOW, when variable groove spacing was introduced) not how the platter drive operates.
To that end, the platter is driven by a drive shaft operated by a transmission that has the gear ratios for its two speeds (33 and 45), which is in turn driven by a 1/8th horsepower synchronous motor running at 1800 rpm. The motor, if operated with no load (or external flywheel), takes over 30 seconds to spin down (nice bearings). That, coupled with an external flywheel and the various bits of rotating mass in the transmission as well as the actual ~17" platter, insure that the platter's motion is very constant. In a machine such as this, the proper function of the drive shaft and whether the platter bearings have been properly lubricated and warmed up (the manual calls for a 20 minute warmup time) has a much greater effect on the platter speed stability than any 'cogging' that might be present in the motor!
Scullys were one of the most popular lathes in the US for a long time, but there are other types such as the Neumann as well. Except for those that use the Technics drive motor, they all run along similar principles.
I've used the Timeline on the Scully; when we were finishing the refurbishment a few years ago I felt it a good idea to see how we were doing. Its pretty stable- but IMO isn't the last word in speed stability or accuracy. It can keep a strobe absolutely still and doesn't vary except when the cutter head touches down to do a cut (which runs about 60 grams of pressure on the stylus). Once touched down the strobe stays put. But the Timeline tells a different story- essentially that the lathe runs ever so slightly slow. How much I've yet to determine since I've not set up the Timeline to present a calibrated assessment. But its clearly close enough that hearing a pitch variation is impossible.
IMO, the big issue of stylus drag affecting speed isn't pitch stability so much as it can induce oscillation of the arm over the stylus- in turn causing the tracking pressure on the groove wall to vary left to right and back. As that happens, it induces to my ear a slight 'shimmer' in the soundstage; when you have a 'table that has really locked-in speed, that shimmer is gone and the soundstage is like that which you hear in reel to reel tape.