We calculate the weak localization (WL) correction to the conductivity of a lateral superlattice (LSL) with Rashba (R)-Dresselhaus (D) spin-orbit interaction (SOI). The superlattice is modeled as a sequence of parallel wires that support tunneling between adjacent sites, leading to the formation of extended Bloch states along its axis and a miniband in the energy spectrum. Our results, obtained by calculating the eigenvalues of the Cooperon operator in the diffusion approximation, indicate that the electron dephasing rate that determines the antilocalization correction is enhanced by a term proportional with the LSL potential and the bandwidth. Within the same formalism, the spin-relaxation rates associated with the localization corrections are found to exhibit a strong anisotropy dictated by the relative strength of the two SOI couplings, as well as by the orientation of the LSL axis.