The transverse electric field which appears in lateral superlattices (SLs) in the presence of a high applied electric field and a low magnetic field H normal to the SL plane is calculated. When the electron energy spectrum is non-additive, the field contains both the Hall field and the spontaneous transverse electric field which exists without H. The field is a multiple-valued and sign-changing function of . The kinetic potential whose minimum corresponds to the stationary state of the non-equilibrium electron gas is used. The magnetoresistance caused by the appearance of a spontaneous transverse EMF is investigated.