Using conventional continuum-based simulation frameworks to model crack initiation and extension can be computationally challenging. As an alternative to continuum-based approaches, particle-based simulation methods are well-suited to handle the discontinuities present during fracture propagation. A well-known particle-based method is the lattice particle method (LPM), which discretizes the system into a set of interconnected particles ollowing a periodic arrangement. Discontinuities can be handled simply by removing bonds between particles. For this reason, LPM-based simulations have been employed to simulate fracture propagation in heterogeneous media, notably in civil engineering and biomaterials applications. However, a practical limitation of this method is the absence of implementation within a commonly-used software platform. This work describes such an implementation of a non-local LPM within the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). Specifically, we implemented a new LAMMPS bond style with a many-body term to tune Poisson's ratios. In order to validate the nonlocal formalism and our implementation of this method within LAMMPS, simulated elastic properties are compared to analytical solutions reported in the literature. Good agreement between simulated and analytical values is found for systems with positive Poisson's ratios. The computational and parallel efficiency of the LPM-LAMMPS implementation is also benchmarked. Finally, we compare the elastic response of a 3D porous structure and an aircraft wing as calculated using the LPM and finite-element analysis.