The macroscopic large-deformation response of mechanical lattice metamaterials is governed by the interaction between the elasto-plastic behavior of the constituent solid phase and the evolving stress distributions within their mesostructures. This interplay gives rise to homogenized stress–strain responses characterized by coupled isotropic, kinematic, and distortional hardening, posing significant challenges for classical phenomenological constitutive models. In this work, we present a compact, data-driven constitutive modeling approach that accurately captures these effects while remaining computationally efficient. Training data are generated from finite element simulations of representative unit cells of truss, shell, and plate lattices with cubic symmetry. The datasets consist of non-proportional random-walk strain paths in the full six-dimensional strain space and the corresponding macroscopic stress histories. A systematic hyperparameter study is performed to investigate the influence of network architecture, training set size, and loading path characteristics on predictive accuracy. The results show that a minimal state cell (MSC) architecture with approximately 5,000 parameters achieves excellent generalization when trained on only 6,000 strain–stress sequences. Using the same fixed architecture, the MSC model is successfully trained and validated for FCC truss lattices, BCC shell lattices, and FCC/SC plate lattices, demonstrating its robustness across different lattice topologies. For reference, an anisotropic Deshpande–Fleck plasticity model is calibrated to the same data, enabling a direct comparison between phenomenological and data-driven approaches. The comparison highlights the superior accuracy of the learned model in reproducing complex, history-dependent responses. The applicability of the MSC model to large-scale simulations is illustrated through hemispherical punch indentation, where simulations employing only a few thousand solid elements closely match the response of detailed shell models with millions of elements. These results demonstrate the potential of compact machine learning–based constitutive models as efficient surrogates for complex lattice metamaterials.