There are a few modes of CNC control of the lathe chuck or spindle.
There is the simple control of spindle rpm which is commanded by the CNC, but it seems you are after the more complex control of also making the spindle into what is known as the C axis because it revolves around the Z.
This is can accomplished in a few ways, all will require an encoder on the final spindle shaft.
Some systems use a VFD on the spindle motor that is capable of this kind of operation, others methods include a separate servo motor to control the spindle when C axis control is desired, this servo motor is usually disabled when normal spindle operation is performed.
All methodes require a servo type of operation.
For just threading and constant surface feed however, a VFD with an encoder is all that is needed, as the Z axis will sync to the spindle via the spindle encoder.