A lathe can't actually replicate itself completely. Specifically, a lathe can only make ways smaller than its own cross slide's stroke. It would also be impossible to make a typical lathe bed on a lathe, though you theoretically could design an unconventional lathe bed that is possible to make on a lathe, even if grossly impractical.
The real starting point for machine precision is rubbing 3 granite plates together.
The real starting point for machine precision is rubbing 3 granite plates together.