Nige
You will need some form of electronic spindle encoder to feed the Arduino, in order to synchronise the rotation of the spindle and the leadscrew stepper motor, if you are considering screw threading. It can be done, it's a bit like an electric gearbox.
If you Google "Electronic Lead Screw" you will find lots of interesting stuff.
Bet you will be the first to do it to an Adept Lathe though.
Mike