CNC on a lathe

Another question for everybody. And for this question I need to
clarify that I'm NOT a machining wiz - in fact I don't even have my
own lathe yet.

If a lathe is converted to CNC, I thought that it would make
machining complex tapers and rounds or spheres much easier. But as I
looked at the current manual devices that cut these shapes - say the
spherical ends - the cutter rotates with the device. Which seems to
make sense because then your cutters' angles are always 'correct' in
respect to the tangency of your cut surface.

For a CNC lathe, how do you go about cutting a spherical end without
changing tool bits?

If this is a stupid question, I do apologize.

-Chris