The way to cut Lunetius is going to depend on what fabric you have chosen to use. If you have enough fabric width you can cut it on the foldSee On the fold in the Sewing documentation. If you don’t, you can cut two halves and later sew them together. To not have to later finish the centre back edge you can cut with the centre back edge on the selvage.
A lot of garments were woven to shape in the Roman era, so this is one aspect where you don’t need to worry about historical accuracy at all, unless you would like to weave your Lunetius to shape.
If you want to learn more about this you can read about it in:\ Granger-Taylor, H. (1982) Weaving Clothes To Shape in the Ancient World: The Tunic and Toga of the Arringatore in Textile History 13 (1), pp 3-25
The further we go back in time, the less extant garments we have to base research on. Often there may be scraps of fabric left behind by stroke of luck but most of our information starts to come from (in archaeology) secondary sources like written texts from contemporaries.
This is especially true for the Roman and Mediaeval eras, not to mention that a lot of the available research is behind a paywall.
We can’t be 100 percent historically accurate, because we’re living in a different time, and everything we use to sew is different now from before. Even fabric is woven in a different way.
How ‘accurate’ you want to be is up to you, there is no wrong way to do this and research is not required -- though it can be fun!