My understanding is that the mixed method (lamp + Balmer lines) was used in ISIS to compensate for the original Ne-only lamp bulbs only having usable lines at the red end. When Shelyak introduced the replacement Ar-Ne bulbs, I was told that method was redundant and I should just use the lamp lines. In my LISA the Ar-Ne bulb produces sufficient lines across the whole spectrum to use for calibration without needing a stellar spectrum. I always had problems getting a good result with the mixed method and found using just the Ar-Ne lines worked much better.
I probably missed it somewhere in the earlier discussion whether John’s lamp has the Ar-Ne bulb. Some of these bulbs can deteriorate over time so it may be worth asking Francois Cochard at Shelyak if the emission line spectrum you get from the Alpy calibration module is what he expects to see. I’ve found Francois very willing to help resolve problems like that.
One small point on an earlier posting by Robin. Robin said “I see the wavelengths I posted (and listed by ISIS in the reports) are the values calculated from the fit, not the true values”. In my experience, the lambda values which ISIS lists in the report are the true wavelength values you give it for the lines. The dlambda values are the corrections it has applied to these values to get the best fit.