....
If I put the lathe on the VFD, everything would work well, I would
switch the VFD with the ON/OFF/BRAKE lever connected to its control
terminals.

It would work great, except:

This is all problem AS LONG AS I do not try to flip the
REV2/REV1/OFF/FWD1/FWD2 switch during running. If I ever do so, the
drive may be ruined as I would switch the motor live with VFD powered.
....

I've got this exact setup on my 10EE. Once/year I forget and go from forward
to reverse. It trips the VFD out. OVC alarm code, IIRC. Just reset the VFD
and go. No big deal.

Karl