The formulation describing the electromagnetic field radiated by a lightning return stroke over a two-layered conducting ground is presented in this paper. The derivation of the Green's functions required to solve the problem is first discussed in detail, and the expressions for the lightning electromagnetic fields are determined. Afterward, an efficient method for the numerical evaluation of the electromagnetic field is proposed. The proposed method is based on a suitable modification of a previously developed model for the evaluation of the fields in the presence of a lossy but homogeneous soil. Particular attention is devoted to the soil reflection coefficient properties, both from a physical and from a mathematical point of view. In part 2 of the paper, the developed approach and numerical algorithms will be used to evaluate the effect of the soil stratification on the radiated fields and to perform the validity assessment of simplified approaches proposed in the literature.