Lengenbachite is a naturally occurring layered mineral formed with alternating stacks of two constituent PbS-like and M2S3-like two-dimensional (2D) material layers due to the phase segregation process during the formation. Here, we demonstrate to achieve van der Waals (vdW) heterostructures of lengenbachite down to a few layer-pair thickness by mechanical exfoliation of bulk lengenbachite mineral. The incommensurability between the constituent isotropic 2D material layers makes the formed vdW heterostructure exhibit strong in-plane structural anisotropy, which leads to highly anisotropic optical responses in lengenbachite thin flakes, including anisotropic Raman scattering, linear dichroism, and anisotropic third-harmonic generation. Moreover, we exploit the nonlinear optical anisotropy for polarization-dependent intensity modulation of the converted third-harmonic optical vortices. Our study establishes lengenbachite as a new natural vdW heterostructure-based 2D material with unique optical properties for realizing anisotropic optical devices for photonic integrated circuits and optical information processing.