Well, thats sorta what "lux" is.
Lux is basically high bright the hotspot is.
Well, the brighter and tighter the hotspot, the further the light will throw. (in most cases)
"Lumens" is the total overall light output. So, you could have alot of lumens, but no throw. IE a flood light. Its putting out alot of light, but its not focused, so it has a low Lux rating.
I dont have the link handy,,, but go look at QuickBeams awsome throw vs. lumens chart.