The lumen is an SI unit which measures brightness.
Putting one light next to another light doesn't make either one brighter.
A lux meter tells the tale.
With one CFL (but could be any light source):
With two equal sized CFLs:
Huh, the reading is essentially identical.
As Julius Sumner Miller said,
WHY is it SO?
Simple, the lux meter is measuring the intensity of the highest energy photons it sees- it is NOT measuring the QUANTITY of photons. Thus- 'lumens don't add'. If you have a 1500 lumen lamp next to another 1500 lumen lamp, the meter will read 1500 lumens. If you have a 1000 lumen lamp next to a 1500, the meter will read 1500.
It is the energy level or intensity of the light which drives photosynthesis. Higher intensity light penetrates foliage better than lower intensity light, as well.
If you need more intensity you get a brighter light, not more dim ones.