In nature, the mechanical properties of several biological systems are controlled by topological features that can span over multiple length scales. Mimicking these architectural features to create man-made lightweight, yet mechanically robust materials have been a topic of extreme interest to the materials science community. Despite their complexity, the fabrication of such topologies is made possible by the emergence of advanced fabrication techniques such as additive manufacturing that can achieve complex architectures at small scales (i.e., nanometer and micrometer). In this work, we report the fabrication and mechanical testing of micro-architected cellular materials with topologies that are inspired by nature. The proposed lattices are based on triply periodic minimal surfaces (TPMS). The lattices were fabricated with feature sizes in the order of several microns using the direct laser writing two-photon lithography technique. These TPMS-based microlattices are shell-based metamaterials with high geometrical complexity. Interestingly, results show that they follow a stretching-dominated mode of deformation and that they are less affected by the change in density as compared to strut-based lattices.