One of the most significant lightning-related quantities is the return stroke current, which is defined as the spatial and temporal distribution of the lightning current after the contact between the leader of the discharge and the ground is established. Gaining information about the return stroke current is of prime importance for the general investigation into the lightning physics as well as for the determination of the correct expression of the electromagnetic field associated with the phenomenon. In this paper we propose an inverse procedure for the reconstruction of the proper waveform of the return stroke current, starting from the measurement of the vertical component of the electric field it produces at different locations on the ground and making use of the integral equation expressing the link between field and current. The ground is assumed to be conductive, and the general Sommerfeld's theory for the vertical antenna radiation over a lossy half-space is adopted for the calculation of the field. It is shown that the unknown current distribution along the channel can be identified if it is suitably expanded by means of a modified basis of Chebyshev polynomials. The proposed approach is validated by means of the numerical simulation of the classical MTLE (Modified Transmission Line Exponential) engineering model, and an analysis on the role played by ground conductivity in the identification process is carried out.