I think you should go search the definitions for yourself. My take on the terms is that LUX requires that the light produce a given amount across an a given area.

The "lumen" is a measure of light intensity for a given "point" that the light beam is collected. The whole thing is voodoo - man - watch out for zombies......

I actually went out re-read primers on "wave theory" and quantum theory to "see" if i could ever understand what light "is." - I don't.

In any case - the most important attribute of a bicycle light is how it illuminates the path or object you are encountering while moving. (not so important if you are standing still) In "theory" the power of a light in not as important as how its beam is projected on the objects you need illuminating.

Good Lux with understanding my meaning.