I used one of mine 4000 Lumen 120° LED light on several cameras, including my Gopro 2 and the 120° beam cover most of the scene, but:
Even in "crystal" clear Sardinian waters a 120° beam 4000 lumen dive light will NOT illuminate anything - except reflecting things - more far than 2 ft during daylight,
while they work nice during night or wreck/cavern/cave dives illuminating big dark spaces.
As AdamHalon already mentioned, due the 180° FoV the GoPro is very picky to use with torches and a more concentrated beam will penetrate more but
create ugly hotspot's in the pictures/videos and the GoPro 2 is not able to focus very near.
LUX is the most useful value for comparing (dive) lights but most of the manufacturers use Watt or Lumen instead of Lux.
A 4000 Lumen torch emit 4000 lumen of light, BUT depending of the reflector or beam width the 4000 lumen may not arrive on the object because of the beam with.
The 160 lumen focus lights in my Z-240 strobes are brighter than the 4000 lumen mangrove light because of it's narrow beam.
Chris