Lattices are architected metamaterials whose properties strongly depend on their geometrical design.The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling.In this work we present a higher-order GNN model trained to predict the fourth-order stiffness tensor of periodic strut-based lattices.The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy.We compare the model to non-equivariant models based on a number of error metrics and demonstrate the benefits of the encoded equivariance and energy conservation in terms of predictive performance and reduced training requirements.