We use a finite element method (FEM) to evaluate the effect of a horizontally stratified two-layer ground on underground lightning electromagnetic fields and their induced currents on the shield of buried cables. It is shown that the azimuthal component of the magnetic field in the upper soil layer is affected by the soil stratification only when this layer is more conductive than the lower soil layer. On the other hand, inside the lower soil layer, this component is always affected by the soil stratification. The vertical electric field in the upper soil layer is mainly determined by the conductivity of the same layer in particular at close observation points. However, this component inside a more conductive lower soil layer is identical to that corresponding to a homogeneous soil with the same property of the lower soil layer. The horizontal electric field inside a stratified ground always takes values in between the electric fields corresponding to one-layer homogenous grounds. We also present a comparison with available experimental data on induced currents of a shielded buried cable and show that, in agreement with recent studies, taking the soil stratification into account allows to improve the late-time response of the induced currents. We also show that the horizontal stratification of soil may result, in some cases, in an enhancement of the induced currents with respect to the case of a homogeneous ground characterized by the electrical properties of either of the two layers.