For a small lathe you would be better using a 4 pole 1500 RPM motor and VFD and turning the frequency up to 100Hz to get 3000 RPM than using a 2 pole and turning it down for lower speed. You can’t increase the current at lower speed due to resistive losses so will get much lower power and torque.
My knowledge from AC motors comes from what I have picked up the last 20 years from reading forums, so maybe I am totally wrong.
A low pole count motor will run at a low max RPM but will deliver a more constant torque at a lower RPM.
A high pole count motor will run at a high max RPM but the torque will decrease significantly when running at lower RPM.
My low pole count AC servos deliver an almost constant torque from 0 to their max (3000) RPM.
My AC spindle motor with VFD delivers a high torque from 200 RPM to 2250 RPM.
My low pole count BLDC motors deliver an almost constant torque from 400 to their max 3500 RPM.
So for more torque at low RPM (threading) I would select a low pole count motor and compromise on the max RPM.