Lattices based on triply periodic minimal surfaces (TPMS) have recently attracted increasing interest, but their additive manufacturing (AM) is fraught with imperfections that compromise their structural integrity. Initial research has addressed the influence of process-induced imperfections in lattices, but so far numerical work for TPMS lattices is insufficient. Therefore, in the present study, the structure–property relationships of TPMS lattices, including their imperfections, are investigated experimentally and numerically. The main focus is on a biomimetic Schoen I-WP network lattice made of laser powder bed fusion (LPBF) processed Ti-42Nb designed for bone tissue engineering (BTE). The lattice is scanned by computed tomography (CT) and its as-built morphology is examined before a modeling procedure for artificial reconstruction is developed. The structure–property relationships are analyzed by experimental and numerical compression tests. An anisotropic elastoplastic material model is parameterized for finite element analyses (FEA). The numerical results indicates that the reconstruction of the as-built morphology decisively improves the prediction accuracy compared to the ideal design. This work highlights the central importance of process-related imperfections for the structure–property relationships of TPMS lattices and proposes a modeling procedure to capture their implications.