I see your logic, but there is an interfering effect you may not have realized....under ideal conditions the light would be constant, i.e. running the lamp on D.C., but off A.C. of various frequencies you will get pulses of light as the arc fires with each half cycle. Your light meters may be effected by this flickering to some extent, but one would expect therm to contain low pass filters which do average it out. At different frequencies, the electrodes of a discharge lamp behave differently....there is less electrode loss at higher frequency, (at very high frequency the electrodes can be bypassed altogether), this makes the lamp more efficient, i.e greater luminous flux at a given power consumption...note I don't mention the current here.
The lamp current is more important when you are trying to match the lamp electrically to the gear...i.e. impedance matching, if this is grossly incorrect, either the lamp or the gear may be damaged. Normally discharge lamps are designed to operate in a narrow arc current range with about a 3% variance each way over many thousands of hours of operation, but if a lamp only needs to operate for a few tens of hours, a 10% variance is probably quite acceptable. Most discharge lamps do not like being either OVER or UNDER powered for long durations and often long durations running under power can damage some lamps more tham lomg durations overpowered by the same amount.
The light output or Luminous Flux is actually quite difficult to measure because you have to collect all the light, going out in all directions, and somehow channel it all into the light meter, this is what those big photometer integrating spheres are for you see in lamp labs at the plants, the white painted inside of the sphere, with the test lamp in the centre and the light measuring device looking in through a small hole with a baffle in front so it can't see the lamp directly, just the light off the spherical surface...but a sample taken from the same direction should suffice for relative measurements.
Now you are making another assumption, that the arc current and luminous flux bear a linear relationship to each other....this is probably not so, but may be partially true over a small increment of current range and luminous flux range....if you take a tiny enough segment of a curved line this can be considered as practically straight...isn't that one of the cornerstones of Calculus?
Generally there is a semi linear relationship between lamp POWER consumption and Luminous flux, but even that is a reallty curly subject to get a grasp on..as an incandescent lamp's power is reduced it luminous flux falls and is effected by TWO factors...the reduction in power AND the movement of the peak spectral power down into the infra-red...se Black Body radiators and Plankain Curves...
For discharge lamps, dimming them is sort of like trying to make a fire burn upside down, bloody difficult, but not impossible. I feel you are trying to control the luminous flux of the SOX 18 so you can obtain various lux levels at an illuminated surface with the nearly monochromatic light...the easiest method, by far, would be to use neutral density filters and run the lamp at its full rating all the time....BUT, it can also be done without fancy filters OR dimming the lamp....simply invoke the old inverse-square law....just move the lamp twice as far away to get illuminance at a surface 1/4 as much, 3 times further away, 1/9th as much etc.
Adjusting (reducing) the arc current will invoke spectral changes like run-up in reverse and increasing it too much will shorten the electrode life...of you want more, use two lamps, or a higher power rated lamp.
If you are really curious and wish to learn as much about lamps as you can, or your time will allow, you could sit down and measure the arc current and the illuminance at a set distance and set angle and vary the arc current, (you need to build adjustable gear for this) and plot the illuminance changes as a consequence on a graph...this will tell you if the relationship is linear of not...but will this be helpful to your ultimate aim, I cannot tell.
A few points about SOX lamps...because the arc tube is "U" shaped, nearly twice as mich light goes out the sides of the "U" as out the edges of the "U". Resonance imprisonment
plays a very significant role in the luminous flux emitted...
The most important things are to learn something new everyday and have fun doing it....