The properties of periodic solid-state materials are frequently modified by the inclusion of interstitial atoms deposited pseudo-randomly throughout the crystal lattice. Accurately calculating overall lattice properties currently requires time-intensive, high-level quantum (typically DFT) calculations, often on 1000s of stochastic lattices. 'Interatomic potential models' (IPM) can mitigate such computational burdens by awarding discrete coefficients to common interstitial geometric ensembles within the wider lattice, and then summing these in a simple regression. Human-designed IPMs however typically take years to be developed. Herein, using molybdenum carbide (Mo lattice, C interstitial added atom) as a model, we show a Crystal Graph Neural Network (CGNet) workflow that can derive near-perfect IPMs from <300 DFT inputs in seconds. Our pipeline (CGNet+CGExplainer) demonstrates high potential for generality in exploring lattice structure-property relations rapidly while maintaining accuracy and interpretability.