Any VFD correctly sized for the motor will work with the Acorn provided it can accept 0-10V analog speed control, which just about most do.
Regards the motor then again correctly sized AC motor which fits the machine should reverse fine, depending on the size of the motor and load then you will need to fit a braking resistor to the VFD.

However, you need to check the lathe can handle being run in reverse, the reason the manufacture probably didn't allow reverse running was because it would spin the chuck off.?

Also, you may be slightly off with your calculations for the motor sizing.? 60Kw Motor would twist even the best-built mini-lathe into a spaghetti mess and dim the lights in the street.