In this paper, a new representation for the lightning channel base current is proposed in terms of the so-called Prony series, obtained by means of a modified time-domain variant of the well-known vector fitting technique. This method allows both to reproduce in an equivalent way previous analytical representations such as Heidler's function and, more interestingly, to obtain a smooth analytical interpolation of measured raw data, in an automatic though tunable way, without the need of filtering, and taking into account the desired behavior of the current for t = 0. Furthermore, a Prony series, i.e., a representation in terms of a sum of exponentials and/or dumped sinusoids, permits us to carry out the computation of the integrals expressing the lightning electromagnetic fields by means of a recursive convolution algorithm, thus reducing the required CPU time. This makes the proposed approach extremely useful for studies of lightning performance of distribution lines, which require the simulation of an appreciable number of cases.