Lightweight aggregate concrete (LWAC) offers significant sustainability advantages due to its reduced density, lower transportation demand, and improved thermal performance. Further reductions in environmental impact can be achieved by decreasing clinker content through the use of alternative cementitious materials. In this context, the present study focuses on the use of a micrometric silica by-product obtained from dunite mining as a partial cement replacement in LWAC. This material is currently stockpiled without commercial application, enabling its valorisation. The development of cement-based materials incorporating novel constituents typically requires extensive experimental testing, for which numerical modelling provides an efficient tool to support material assessment. Among the different modelling scales, mesoscale approaches are particularly suitable for LWAC, as they explicitly capture the material heterogeneity arising from the interaction between lightweight aggregates and the cementitious matrix. In this work, the mechanical performance of LWAC incorporating partial cement replacement by this dunite mining by-product is investigated at the mesoscale, where it is 3D modelled as a heterogeneous two-phase system composed of mortar and lightweight aggregates. Representative Volume Elements (RVEs) are generated with randomly distributed spherical aggregates following a take-and-place strategy consistent with the experimental mix design and aggregate granulometry. Virtual uniaxial compression tests are performed using the Finite Element Method (FEM), with nonlinear mortar and aggregate behaviour described by the Drucker–Prager model in compression and the Willam–Warnke model in tension. The proposed framework is applied to LWAC mixtures with different levels of cement substitution (5% and 10%), and the numerical predictions are validated against laboratory uniaxial compression tests. In addition to compressive strength and stiffness, the model captures cracking and crushing mechanisms at the mesoscale. The results demonstrate the potential of the proposed numerical–experimental approach as an efficient tool for the assessment of sustainable LWAC.