Since the seminal work of Cundall and Strack (1979), the Discrete Element Method (DEM) has now become accepted as a key tool amongst researchers exploring the fundamental behavior of granular materials. Along with a sustained increase in the number of publications documenting use of DEM in research, intensive development of new open-source and commercial DEM codes has taken place in the last decades. The credibility of these software packages depends on their capacity to replicate physical observations and to reproduce theoretical expressions. Researchers often calibrate DEM codes against laboratory data to gain confidence about their predictions, however, theoretical verifications at the macro and particle levels are often omitted or not explicitly documented or acknowledged. The validation of DEM codes against theoretical expressions is fundamental to guarantee reproducibility and generality of the software, and to avoid bias in more complex simulations. In this article, a dataset providing numerical simulation data along with input files is presented. The dataset relates to a series of theoretical validation approaches, previously documented in the literature, that were here applied to verify the open-source DEM code LAMMPS. The ability of LAMMPS to capture the macroscopic behaviour of granular packages is evaluated by shearing a face-center-cubic (FCC) array of monosized spheres. The calculation of particle translational/rotational motions and forces/torques is checked by considering a clump rolling down an inclined plane. Additionally, the stress-strain behavior of Toyoura sand under "drained" and "undrained" shearing is characterized by a series of LAMMPS outputs. The dataset collected from these simulations can be employed by users to benchmark new or existing DEM codes. Both the LAMMPS input scripts and the simulation results for all the cases are available in a public repository.