The relationship between a lathe's accuracy and a long range hunting rifle's accuracy is tenuous at best.
If my 7mmRemMag chamber that is 0.0050" off center of the lathe when done, shoots 0.75" groups at 100 yards, then the difference between a $3K Chinese lathe that has 0.0005" runout and a $75k Monarch that has 0.00003" run out, is ...
$75K - $3K = $72K cost change
[.0005"] [.75"]/[.005"] = .075" Chinese group size
[.00003][.75]/[.005"] = .0045" Monarch group size
.075" Chinese group - .0045" Monarch group = .0705" group improvement with Monarch
[$72K Monarch upgrade]/ [.0705" Monarch group improvement] = $1,021,276.60 per moa improvement.
What does it all mean?
Ammo concentricity is important, as the ammo is inserted with random rotational orientation, but chamber concentricity has constant rotational orientation, and so is less important. This often confuses gunsmiths, and they dial in both ends of a barrel to get the bore concentric and parallel with the lathe spindle to within .0001".
I have done it.
Don't fall for that accuracy ritual.
You can get beat at the range in a match with someone who chambered on a drill press.