This paper generalizes the theory of the electron runaway and runaway discharge to the case of a laminar electric field at an arbitrary angle to the magnetic field and derives the relevant threshold conditions. It is shown that the conditions of the runaway process depend on the angle between the electric and magnetic fields, and the ratio of their magnitudes. In fact, the geomagnetic field hinders the development of runaway breakdown in the atmosphere. This effect has implications for runaway discharges in the atmosphere caused by low—altitude lightning. The runaway discharges manifest themselves as fluxes of γ rays, as previously observed by the detector aboard Compton Gamma Ray Observatory. The geomagnetic field plays a significant role in the runaway discharge due to thunderstorms for heights above 20 km, where the cyclotron frequency of relativistic electrons exceeds their collision frequency. This effect depends on the angle between the electric and magnetic fields. Since the static electric fields from thunderclouds are directed almost vertically, one can expect a significant difference in the properties of high-altitude discharges occurring at equatorial and high-latitude regions.