Nonlinear magnetotransport in a two-dimensional electron gas in one-dimensional lateral lattices fabricated from a selectively doped GaAs/AlAs heterostructure is investigated. One-dimensional potential modulation is imposed on the two-dimensional electron gas by means of a set of metal strips formed on the planar surface of Hall bars. The dependences of the differential resistance rxx on the magnetic field B < 0.5 T are studied at a temperature T = 1.6 K in lattices with a period of a ≈ 200nm. It is shown that periodic oscillations in rxx(1/B) occur in such lattices under the action of a current-induced Hall field due to Zener tunneling between Landau levels. Interference is found between Zener oscillations and commensurability oscillations of rxx in two-dimensional electron systems with one-dimensional periodic modulation. The experimental results are qualitatively explained by the role of Landau bands in nonlinear transport at large filling factors.