(highlight:: Actually no, and we are very lucky because of that. You can produce a one off lathe that is much more precise than everything that was done before. It would take extraordinary amount of effort and will take long time but it can certainly be done.
This is where I'd like to explain two very important principles of precision: Selective correction and Averaging.
Suppose you live in the stone age and the wheel hasn't been invented yet. You want to make yourself a spear but you do not have a perfectly straight stick. Bear in mind that the quality of your weapon tells a lot about your skill as a warrior and nobody respects a warrior with a crooked spear. The quality of your weapon is very much a status symbol. Perfectly straight sticks do not grow on trees and there are no spear shops to go buy one from. So what do you do?
You can certainly get a big old trunk of wood and try to hew a straight stick out of it by cutting away everything that is not a straight stick. This however does not produce a strong weapon because you have to cut across the grain of the wood.
The secret here is to take the strongest stick possible, even though it is crooked and then try to straighten it without cutting across any grain. You do this by sighting along the stick to see what the most crooked part is, then you heat that part over the fire and then you straighten it over your knee until it is flat. If you do this many many times, you will gradually end up with a straighter and straighter stick.
In other words, you correct the most visible error selectively, until you end up with a much more precise product. Selective correction of error!
I can give you examples to make it more clear.
Here are a few dudes straightening bits of bamboo using heat.
Here is the same principle applied in a much more modern way to straighten a metal shaft. It is exactly the same principle though.
When you combine this principle with the principle of reducing errors trough averaging you get to Metal Scraping This is the art of creating incredibly flat and straight surfaces by hand. This is how the most precise lathes are manufactured even today. And since it is a manual process you can make arbitrarily big machines with it.)
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