To begin with, establish a DOC that works well with the tool, the lathe, and the material. This is easy enough to do during roughing, and as it's mostly a rule of thumb, you don't need to be too scientific -- all that matters is that when you take that cut, the results are accurate to .001. For my 14" lathe, with trigon (WNMG) inserts, on mild steel, this is around .020.
When making a part, take it down to double this measurement, then take two cuts of equal depth, measuring between the first and second as a sanity check if the measurement is critical.
On my 12×36 lathe I hog down in 0.020 (like above) until I am 3×DoCs away from the desired diameter (+/- a couple of thou) and take an accurate measurement (micrometer)
I then dial in 1/3rd of the difference between where I am and where I want to finish and take that cut.
I then measure to see how much actually came off and divide that by 1/2
I then dial in the 1/2 remaining and take the cut.
I then measure to see how much actually came off and calculate how much is left. Based on the previous 2 cuts and subsequent measurements I adjust the final cut.
So, if I had 59.5 thou to go, I would dial in DoC=20 and take a cut, this might come out still needing 48.5 though (1 thou more than I though I dialed in)
Half of the 48.5 is 19 thou so I dial this in take the cut and then measure.
So, now I find I have 19.7 thou to go (0.2 less than dialed in). So, I dial in 19.7-1.0+0.2 = 18.9
Notice that you only dial in fractions of a thou on the last cut.
The change in tool pressure from 20 thou to 19 thou to 18.9 thou is essentially negligible, and what makes this procedure self correcting.
When I used the 2 tries method I would end up +/- 0.001,5" and when I use the 3 tries method I generally hit +/- 0.000,7" or better.
But watch out !!:: when you hit a number this precisely, the number will change as the part cools down (overnight, for example.)
I once hit a target of 2.000,0" on the lathe and came back the next morning to find it was 1.999,7" ?!?