The description and validation of an ImageJ open-source plugin to numerically simulate and reconstruct digital lensless holographic microscopy (DLHM) holograms are presented. Two modules compose the presented plugin: the simulation module implements a discrete version of the Rayleigh-Somerfield diffraction formula, which allows the user to directly build a simulated hologram from a known phase and/or amplitude object by just introducing the geometry parameters of the simulated setup; the plugin's reconstruction module implements a discrete version of the Kirchhoff-Helmholtz diffraction integral, thus allowing the user to reconstruct DLHM holograms by introducing the parameters of the acquisition setup and the desired reconstruction distance. The plugin offers the two said modules within the robust environment provided by a complete set of built-in tools for image processing available in ImageJ. While the simulation module has been validated through the evaluation of the forecasted lateral resolution of a DLHM setup in terms of the numerical aperture, the reconstruction module is tested by means of reconstructing experimental DLHM holograms of biological samples.