I spent many years as a machinist and to hold a tolerance of .0001 is very, very hard and when using hand measuring tools everyone's feel is different and must be done with an optical comparator.
For a lathe to follow that tolerance the compound cross slide dial would have to be one to one which means moving the dial 1 turn removes .001 from the diameter and I have not seen one that reads .0001.
Lathes made in the 40's to get that close, I believe it would have to be hand finished.

David