Lightning strikes can seriously affect the reliability and availability of electrical infrastructures. The computation of lightning-electromagnetic fields represents one of the most crucial steps in the evaluation of the induced effects; thus, having at disposal accurate and efficient dedicated tools is essential. This paper proposes a new approach for the lightning-electromagnetic fields computation above a perfectly conducting ground. The proposed approach does not involve any assumption either on the channel-base current waveshape or on the attenuation function of the current along the channel. Integrals are expanded in series of exponential functions (Prony series) which makes them analytically solvable. The proposed approach results in a speed up of the computational time by a factor of 10 to some hundreds with respect to classical numerical approaches. The proposed method is validated against the classical formulas obtained through numerical integration for different channel-base current waveforms, attenuation functions and observation points.