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Short-duration gamma-ray bursts (SGRBs) are widely believed to be powered bythe mergers of compact binaries, such as binary neutron stars or possiblyneutron star-black hole binaries. Though the prospect of detecting SGRBs withgravitational wave (GW) signals by the advanced Laser InterferometerGravitational-Wave Observatory (LIGO)/VIRGO network is promising, no known SGRBhas been found within the expected advanced LIGO/VIRGO sensitivity range forbinary neutron star systems. We find, however, that the two long-short GRBs(GRB 060505 and GRB 060614) may be within the horizon of advanced GW detectors.In the upcoming era of GW astronomy, the merger origin of some long-short GRBs,as favored by the macronova signature displayed in GRB 060614, can beunambiguously tested. The model-dependent time lags between the merger and theonset of the prompt emission of the GRB are estimated. The comparison of suchtime lags between model predictions and the real data expected in the era ofthe GW astronomy would be helpful in revealing the physical processes takingplace at the central engine (including the launch of the relativistic outflow,the emergence of the outflow from the dense material ejected during the merger,and the radiation of gamma rays). We also show that the speed of GWs, with orwithout a simultaneous test of Einstein's equivalence principle, can bedirectly measured to an accuracy of $\sim 3\times 10^{-8}~{\rm cm~s^{-1}}$ oreven better in the advanced LIGO/VIRGO era. The Astrophysical Journal, Volume

GRB/GW association: Long-short GRB candidates, time-lag, measuring gravitational wave velocity and testing Einstein's equivalence principle