Hi Clotilde,
Thanks for your reply. in fact I am writing a python code out of Rhino/Grasshopper environment to calculate Color Rendering Index. So, I wanted to understand how Lark does the sky generation step.
And I know that “the spectral sky model is still the largest uncertainty” 
This is how the diffuse irradiance is weighted by Lark when b1,b2,b3,g1,g2,g3,r1,r2,r3 are the channel outputs and v_ parameters are the photopic coefficients for each channel:
sum9 = b1v_b1 + b2v_b2 + b3v_b3 + g1v_g1 + g2v_g2 + g3v_g3 + r1v_r1 + r2v_r2 + r3*v_r3
diffuse = diffuse/ sum9
sum9 is usually below one (e.g. 0.836 based on D65 SPD) and by dividing the diffuse irradiance by this, you basically use a greater value. This is the part I don’t understand how it helps.
I still think, Lark has the problem with the R G B values in skyfunc glow (which are not summing up to 1)
In order to avoid gen_reindl, I used another gensky option (-r) which involves solar radiance.
years ago Greg said: “to compute the solar radiance (-r) from direct normal irradiance (DNI in wea or epw file), divide the normal irradiance by 5.98e-5, which is the number of steradians in a 0.5 degree source like the sun”
On the same page Greg recommend "multiplying values to the -r and -R options by:
208/179 the ratio between the sun’s efficacy and the standard Radiance factor
Likewise, values to the -b and -B options should be multiplied by:
110/179 the ratio for sky radiation efficacy over the standard Radiance factor".
Later, Francesco Anselmo pointed out D65 efficacy of 203 lm/W (here).
So, I am wondering if this is a shortcoming of Lark tool? and if I need to apply them regarding the type of sky (D65, D50, D70, …) and the SPD data selected by the users?
This is a very good point, I am trying both gendaylit and genutahsky.
Thank you for sharing your experience with me.
Fazel