This is a pretty good heuristic in my experience too, at least for most lights we encounter. Assuming no atmospheric scattering, 1/3 ANSI distance is equivalent to 2.25 lux on target.
With extreme throwers, atmospheric scattering becomes significant. This discussion actually motivated me to learn more about it and make a usable distance calculator that accounts for atmospheric losses: Calculator for usable throw
For example: if a light has a ANSI range of 3km, then your heuristic (2.25 lux on target) gives 1km of usable range under ideal conditions. If the air quality isn’t so great with only 10km of visibility, then the observed illuminance drops to 2.25 lux noticeably earlier, at 747m.