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The evaluation of the electromagnetic field radiated by a lightning stroke is of essential importance for the study of the interaction between lightning electromagnetic fields and power lines, or other sensitive installations. A fast algorithm for calculating the fields generated by a vertical electric dipole over a lossy ground, which can be expressed by the well-known Sommerfeld integrals, is presented in this paper. The integrals are decomposed into two parts. One part can be calculated by a recursive analytical expression, and the other part can be evaluated numerically due to the fact that the extracted integrand damps rapidly with the help of the asymptotic extraction technology. A comparison with some approximate formulas is performed in detail with variable parameters, such as the soil parameters, the geometry, and the excitation frequency of dipole, which shows very good agreement as far as the lightning field is concerned. The technical merit of the proposed approach is its universality, which can be applied for arbitrary parameters, and its computing time is still competitive.