A solution is presented for the electromaginetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense: no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additonal atribute of being specified in closed form in terms of elementary function. Thi solution is discussed from thepoint of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compred with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.