Batteries with high energy densities become essential with the increased uptake of electric vehicles. Battery housing, a protective casing encapsulating the battery, must fulfil competing engineering requirements of high stiffness and effective thermal management whilst being lightweight. In this study, a graded lattice design framework is developed based on topology optimisation to effectively tackle the multidisciplinary objectives associated with battery housing. It leverages the triply periodic minimal surfaces lattices, aiming for high mechanical stiffness and efficient heat dissipation considering heat conduction and convection. The effectiveness of the proposed framework was demonstrated through the battery housing design, showcasing its ability to address multidisciplinary objectives as evidenced by the analysis of the Pareto front. This study identifies the potential of lattices in lightweight applications incorporating multiphysics and offers an efficient lattice design framework readily extended to other engineering challenges.