Not rocket science or I couldn't do it. I set the barrel up in the lathe chuck on one end and the live center on the other end. My 3 jaw chuck is corrected to .0003" on a lathe alignment bar, so I rarely use the 4 jaw.
I indicate the muzzle end on the live center (BesTest Last Word), rolling the barrel away from me by hand. Then indicate the middle of the barrel. I record the t.i.r.'s and then turn the barrel around and put the muzzle end in the chuck and indicate the breech end on the live center. Move to the middle again and indicate it again. If there is any difference at the middle, I just average the readings. Like I said, not rocket science and not perfect, but only takes about 10 minutes and it tells me how straight the O.D. is and how concentric to the bore it is at the ends. Over the space of 10-11 yrs I have done a total of about a dozen Liljas, Harts, Shilens, 1 Krieger, 1 Brux, 1 Lawton, and this Bartlein. Also some factory take-offs out of curiosity.
I have never had a perfectly straight or true barrel.
If the breech end has .001" or more runout, I turn it true while it's on the live center. The muzzle end is a little more trouble. I set it up on the live center and turn it true about 1/2" in front of where the crown will be, then use that to indicate in the muzzle threading or crowning setup, then part it off. Like I said, more trouble, particularly when I have to use the steadyrest and make an interim setup. Depends on how much longer the blank is than the finished length. The closer they are, the easier the setup.
The Liljas have averaged being the straightest, the factory barrels the worst. One ran out .055" in the middle. Tomato stake.
The worst runout on a premium barrel was .0075" in the middle. The finished rifle (.338 Excalibur) hammered at 1K, so that amount of runout didn't appear to hurt it.
I don't have a set of range rods, so I fell back on this system.
Sorry about getting long-winded, but wasn't real sure I understood the question, so went into considerable detail.
Poorboy process, not for benchrest but works well for me. A couple of them shoot in the teens, a few in the 20's, most are sub 1/2 m.o.a., a couple just sub m.o.a.
Good shooting, Tom