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tokens: fixed tile must be smaller than the image separations, which are not known a priori. The sky area spanned by strongly lensed images, however, is ≲arcsec 2 ( Schneider et al. 2006 ; Collett 2015 ), and investigating it at such fine resolution is highly time-consuming. Nevertheless, when both galaxies or galaxy clusters and microlenses are involved, a complete solution of the system requires identification of strongly lensed and microlensed images. In addition, the overall potential may vary profoundly on short length scales. This is particularly true when many microlenses are involved: standard integrators may stall and oscillate between points corresponding to nearby solutions without converging. Finally, gravitational-wave analysis is performed using signal templates predicted by general relativity (GR). The inference of compact source parameters relies on matching gravitational-wave detector strains to a bank of known gravitational waveforms ( Allen et al. 2012 ). This method allowed LIGO and Virgo to unveil a stellar-mass population of binary black holes and produce a catalog of their properties ( Abbott et al. 2019a ), to perform tests of GR ( Abbott et al. 2016c , 2019b , c ), and to detect a binary neutron star coalescence ( Abbott et al. 2017 ). However, lensed signals resulting from the superposition of multiple images can differ significantly from unlensed GWs. As a consequence, matched filtering of lensed GWs with unlensed templates could result in missed detections or possibly biased measurements of the binary parameters. Lensed gravitational waves might also constitute a probe of microlensing. Even when microimages are as close as microarcseconds, observable beating patterns may originate in the GW signal if the time delays between the images are higher than the millisecond time resolution of the interferometers ( Lai et al. 2018 ; Abbott et al. 2019a ). Thus, lensed templates might unveil microlenses and dark matter substructures on the path traveled by the wave ( Liao et al. 2018 ). Therefore we must be able to predict GW signals from arbitrary lens configurations. LENSING GW has been designed to address these necessities: on the one hand, it implements a new solver tailored to handle very different scales in the lens potentials; on the other hand, it supplies unlensed and lensed GW signals from arbitrary lensed systems through dedicated modules. Such lensed waveforms can serve as injections in parameter estimation (PE) studies to demonstrate the inference of astrophysical parameters of lensed compact sources through Bayesian analysis. We will demonstrate Bayesian PE of lensed systems solved with LENSING GW in a follow-up study (Pagano et al., in prep.). The source code of LENSING GW and examples are hosted on GitLab 2 . 3.1. Lens equation solver The numerical solver implemented in LENSING GW introduces two novelties: a two-step procedure designed to simultaneously resolve strongly lensed images and microimages, and a dedicated