A light emitting apparatus comprises: an LED-based light source; a spherical, spheroidal, or toroidal diffuser generating a Lambertian light intensity distribution output at any point on the diffuser surface responsive to illumination inside the diffuser; and a base including a base connector. The LED based light source, the diffuser, and the base are secured together as a unitary LED lamp installable in a lighting socket by connecting the base connector with the lighting socket. The diffuser is shaped and arranged respective to the LED based light source in the unitary LED lamp to conform with an isolux surface of the LED based light source. The base is operatively connected with the LED based light source in the unitary LED lamp to electrically power the LED based light source using electrical power received at the base connector.