We investigate the propagation of Lg waves in laterally varying crustal structures by numerical simulation. The method of calculation is formulated in terms of boundary integral equations where the Green's functions are evaluated by wavenumber summation. The approach is well suited to study the propagation of seismic waves in a layered medium where the interfaces are flat in some regions and irregular in others. We investigate the effect of a crustal fault with vertical offset and study the case of a lateral change in crustal thickness. The results show that the Lg wave amplitude is only slightly affected by the presence of these heterogeneities. They confirm the robustness of Lg wave propagation in presence of lateral heterogeneities observed in other numerical simulations. They show that large-scale geometric features of the crust cannot account alone for the strong attenuation of Lg waves observed in many regions. The results also suggest a possible relation between the level of Lg wave coda and the degree of roughness of the Moho. They further indicate the importance of backscattering and suggest a possible use of the backscattered wave field to map strong crustal heterogeneities.