An isotropic radiator is a theoretical point source of electromagnetic or sound waves which radiates the same intensity of radiation in all directions. It has no preferred direction of radiation. It radiates uniformly in all directions over a sphere centred on the source. Isotropic radiators are used as reference radiators with which other sources are compared.
Whether a radiator is isotropic is independent of whether it obeys Lambert's law. As radiators, a spherical black body is both, a flat black body is Lambertian but not isotropic, a flat chrome sheet is neither, and by symmetry the Sun is isotropic, but not Lambertian on account of limb darkening.
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