9 microns is .00035″.
There are a lot of different models of Doosan lathes.
I have one that is geared between the servo and the ballscrew, using only the motor encoder for feedback. It is a lot more unpredictable than most when starting from cold, but that lathe will still do +/- 9μm without excessive monitoring and adjustment.
I would assume that most Doosan lathes are at least as good as this one.