Yes, you are right - I was thinking only of the non-linearity of lux for distance comparisons (i.e. "throw"), but instead wrote for an output comparison in that sentence. I will revise that - I meant to say for half the distance (not twice the output), lux will score will be four times higher.You have it backwards here, lux is the linear quantity, throw is the non-linear quantity. Double current in a led and you get (roughly) double power consumption, double lux, double lumen and 1.4 times the throw.
I.e. everything follows a linear relationship, except throw (The led conversion of current to brightness is not completely linear).