Your eyes are decieving you. If you move the spheres from the 3 pictures together you will very clearly see that the areas are the same color when single light and brighter when double lit. If you want to make it look nicer I suggest you add a whole arc of light sources between the current ones.
You've saturated one colour channel in the image; turn down the brightness a bit and see what happens.
It's a perceptual effect called Mach banding.
You are also very likely viewing the images in the wrong color space. Your ray tracer is doing the lighting math in a "linear" space, but then you are almost certainly viewing those images on a display with a nonlinear response, and therefore not even seeing the correct results. This could easily be making the Mach bands much more prominent than if you were displaying them properly. Try learning about gamma correction.
Are you sure your lighting directions are both normalized?
May be worth it to throw an assert in there.