The self-assembly of heterogeneous mesoscale systems is mediated by long-range interactions, including van der Waals forces. Diverse mesoscale architectures, built of optically and morphologically anisotropic elements such as DNA, collagen, single-walled carbon nanotubes, and inorganic materials, require a tool to calculate the forces, torques, interaction energies, and Hamaker coefficients that govern assembly in such systems. The mesoscale Lifshitz theory of van der Waals interactions can accurately describe solvent and temperature effects, retardation, and optically and morphologically anisotropic materials for cylindrical and planar interaction geometries. The Gecko Hamaker open-science software implementation of this theory enables new and sophisticated insights into the properties of important organic/inorganic systems: interactions show an extended range of magnitudes and retardation rates, DNA interactions show an imprint of base pair composition, certain SWCNT interactions display retardation-dependent nonmonotonicity, and interactions are mapped across a range of material systems in order to facilitate rational mesoscale design.