GRB 111005A, a long-duration gamma-ray burst (GRB) that occurred within a metal-rich environment that lacks massive stars with MZAMS >= 15M(circle dot), is not coincident with supernova emission down to a stringent limit and thus should be classified as a "long-short" GRB (lsGRB; also known as an SN-less long GRB or hybrid GRB), like GRB 060505 and GRB 060614. In this work, we show that in the neutron star merger model the non-detection of the optical/infrared emission of GRB 111005A requires sub-relativistic neutron-rich ejecta with a mass of <= 0.01 M-circle dot, which is (significantly) less massive than that of GRB 130603B, GRB 060614, GRB 050709, and GRB 170817A. The lsGRBs are found to have a high rate density and the neutron star merger origin model can be unambiguously tested by the joint observations of the second-generation gravitational-wave (GW) detectors and the full-sky gamma-ray monitors such as Fermi-GBM and the proposed GECAM. If no lsGRB/GW association is observed in the 2020s, alternative scenarios have to be systematically investigated. With the detailed environmental information achievable for the nearby events, a novel kind of merger or explosion origin may be identified.