Watt-hours per square meter and lux-hours are two ways of describing the energy that light transmits. The first, watt-hours, considers the light source's total power output. Lux-hours, however, describes perceived luminous intensity, in terms of how much light the human eye observes. Many calculations specify a direct correlation between the two, assuming light's wavelength to be 555 nanometers, which is the wavelength that's the most visible. At other wavelengths however, you must also consider the luminous efficacy, which describes the eye's relative sensitivity to the light.
Look up the eye's sensitivity to the light's wavelength (V(λ)) from the first table in the first link in Resources. If, for instance, you are converting the Watt-hours per meter squared of 640nm light, you'll see that the eye's relative sensitivity to it is 0.175.
Multiply the light's Watt-hours per meter squared by the eye's relative sensitivity to it. If, for instance, you are converting 200 Wh/sq.m -- 200 x 0.175 = 35.
Multiply this answer by 683 -- 35 x 683 = 23,905. The light produces 23,905 lux of illuminance.