It is over years ago since I built my LHIRES but just checked and I see I actually just moved both washers to the same side. Take care to tighten the screws evenly and not to tighten too much as it brings the lens into direct contact with the metal holder. I would only do it if you are seeing significant shifts in the lines backwards and forwards as the lens is rotated. Presumably the problem in my case was uneven thickness of the washers. I did it to prove what was going on. It worked so I left it rather than trying different washers.
I suppose you could use the double line for calibration if you can identify the wavelengths. You could check Richard Walker’s Atlas to see if they are identified