A CNC rotary axis cannot "spin like a lathe", and here's why:
Stepper motors are made to move in steps, not rotate continuously. Even if you can get them to spin with a pulse generator, they have so little torque, they are useless. A motor, or a high end servo with encoder (like big$ cnc lathes have) would be required to turn the 4th axis to enable spinning.
Lets assume you could get the rotary to spin by adding a 3 phase motor with VFD to control RPM. You now have an X, Y and Z mechanical system that is designed to cut in the 1-400 ipm range, depending on model. Normal turning is done in the 1500-2500 rpm range, yielding an average of 6000 to 20,000 inches per minute at the surface with a 1 to 4" blank. Much more than the gantry, X and Z components are built to withstand.
That said, many, even most think that the rotary needs to spin freely to accomplish a turning type profile. Look over the one in this link: https://youtu.be/9bLnP9R7bE0
This is a rotary coordinates type file, just like all rotary files. It was done in VCarve Pro with a 2D profile and a little bit of post processor trickery. Even tho there are few, if any other examples of this happening, at least verified on video, this was done to prove that it can be done using the tools we all have.