Triply periodic minimal surface (TPMS) lattice metamaterials [1], a category of architected cellular materials, have received significant interest recently due to their versatile multifunctional properties and the rapid advancement of additive manufacturing technologies. Nonetheless, explicitly modeling these lattices for structural applications aimed at enhancing mechanical properties remains computationally very expensive. This study introduces a macroscopic constitutive model capable of predicting the anisotropic elastic-plastic-damage behavior of these lattices, including its numerical implementation via the finite element method. The proposed constitutive model incorporates a cubic symmetric elasticity model, a modified anisotropic Hill’s plasticity yield surface, and an anisotropic damage model, both of which capture the asymmetric behavior of lattices under tensile and compressive loads. The framework is validated by predicting the elastic-plastic-damage response of Schoen’s I-WP sheet-based TPMS lattice (IWP-s) at 28% relative density [2] under various multiaxial loading cases, achieving excellent agreement with an explicit micro-mechanics model of the lattice. Additionally, a cantilever beam problem comprising of multiple IWP-s lattices demonstrates an excellent match between the latticed beam’s response and the macroscopic model with a continuum beam structure (macro-mechanics model), reducing computational time by up to 2778 times. The current proposed micro-macroscopic modeling framework enables the development of computationally efficient elastic-plastic-damage constitutive models for various types of lattice metamaterials, enabling an effective computational analysis of their behavior under complex loading conditions. This proves particularly valuable for applications involving large assemblies of these lattices, significantly reducing the computational cost and power requirements.