I think I might have found the correct answer:
Referring to this paper:
The paper below describes the following formula for dimensioning a light source for proper exposure:
L = ( d2 x N2 x C ) / ( S x t )where
L is LED intensity in Lux;For example, given a subject distance of 2 meters, f/2.8, ISO 400, 1/30 sec exposure, and C=200, we need a light source producing 470.4 Lux.
d is subject distance in meters;
N is aperture in f-stops;
C is an arbitrary constant chosen by manufacturers of exposure meters to reflect their view of what represents "correct exposure". Common values seem to be in the 180-250 range;
S is sensor sensitivity in ISO;
t is exposure time in seconds.