Not yet reviewed by Pith; the record is open.

Next-generation ground-based gravitational-wave (GW) detectors are expected to detect millions of binary black hole mergers during their operation period. A small fraction ($\sim 0.1 - 1\%$) of them will be strongly lensed by intervening galaxies and clusters, producing multiple copies of the GW signals. The expected number of lensed events and the distribution of the time delay between lensed images will depend on the mass distribution of the lenses at different redshifts. Warm dark matter or fuzzy dark matter models predict lower abundances of small mass dark matter halos as compared to the standard cold dark matter. This will result in a reduction in the number of strongly lensed GW events, especially at small time delays. Using the number of lensed events and the lensing time delay distribution, we can put a lower bound on the mass of the warm/fuzzy dark matter particle from a catalog of lensed GW events. The expected bounds from GW strong lensing from next-generation detectors are significantly better than the current constraints.