Full-scale CFD simulations or experiments across wide operating conditions are often impractical due to their high computational cost and experimental complexity. Architected lattice structures, enabled by advances in metal additive manufacturing, have shown enhanced fluid-dynamic performance, including improved heat transfer and flow stabilization. However, accurately resolving flow through their complex geometries requires prohibitively expensive high-resolution CFD. Rapid and accurate surrogate models are therefore essential for iterative design and optimization. While recent machine-learning approaches enable efficient flow prediction, most remain limited to simple geometries or exhibit poor generalization to unseen conditions. To overcome these limitations, this work proposes a physics- and geometry-informed neural operator framework trained on a high-fidelity CFD dataset of lattice flows. Neural operators naturally model PDE solution mappings from boundary conditions and geometry to full-field responses. The proposed approach predicts fluid-performance fields directly from STL geometry and boundary conditions, and is systematically compared with state-of-the-art physics- and geometry-informed models. Without retraining, the model achieves 93.09% accuracy in pressure-field prediction across varying inlet conditions and previously unseen lattice geometries, demonstrating strong generalization. Overall, this framework provides a scalable and reusable surrogate for lattice-flow prediction, offering a practical alternative to computationally expensive CFD and enabling accelerated design and optimization workflows.