I don't think you understand anything I have said
It is an isotropic surface - it radiates intensity equally in all directions
Lambertian surfaces do *not* radiate intensity equally in all directions - they radiate intensity proportional to cosine(viewing_angle)
Radiance depends on viewing angle
As the viewing angle increases the projected area of the emitter decreases and the radiance increases
When you COMBINE Lambertian reflectance's cosine term with radiance's 1/cosine term you get CONSTANT RADIANCE
You seem to believe that both radiance *and* intensity are constant!
your point that "radiance is independent of surface orientation" is simply completely wrong
radiance can ONLY be measured with respect to surface orientation!