This paper studies the electromagnetic field radiated by a return stroke, considering even the case of a direct lightning on an aircraft, in the Fraunhofer region. The work here presented is an analysis of a complete discharge case, considering the electric field due to some charged clouds, the presence of a conductive airplane immersed in this external electric field, the channels related to the lightning paths, and the interactions of the field due to the lightning return stroke with a far field located victim system. It could be divided in several steps. Firstly, the cloud-generated electric field has been calculated, and a particular model of the clouds has been introduced. For what concerns the geometrical considerations, a Koch's snowflake shaped cloud has been chosen, in order to achieve a complex geometrical model. To better fit this model with the reality a non-symmetric cloud has been created. Then, a simple aircraft model, according to those reported in literature, has been introduced. The conductive structure of the aircraft interacts with the atmospheric electric field and modifies its distribution. Furthermore, applying a boundary panel method, frequently used in subsonic incompressible aerodynamics, Laplace's equation for the electrostatic potential in the considered domain has been computed, taking into account the presence of the metallic structure. Finally, the inception points on the outer surface of the aircraft are calculated and highlighted. Beginning from those points, in which the probability of discharge is higher, a suitable lightning channel has been created, and the shape of the jagged field signal has been correlated to the tortuous path discharge, even considering the presence of branches. The total electric field given by the first discharge from the cloud to the airplane, by the second discharge from the aircraft to the ground and by the current flowing along the fuselage has been computed and calculated in a far field located observation point.