Yes in that case impressively close !
I have to confess the idea of using the superimposed lamp lines came from Christian Buil,the objective being to solve the issue of shifts due mechanical flexure in the LHIRES.
about half way down (In French)
Those particular “Filly” lamps are not around any more but you would only need one reference line to correct the offset in the dispersion equation measured using the internal LHIRES lamp as you did using the water line so chances are even a neon lamp would do. The intensity of the lamp line(s) has to be adjusted to match the exposure needed for the star (not a problem in this case with bright Deneb) eg by adding some filtering material in front or perhaps in a more sophisticated setup, by electronically pulsing it on and off.