We investigate the ability of the Large Synoptic Survey Telescope (LSST) to discover kilonovae (kNe) from binary neutron star (BNS) and neutron star-black hole (NSBH) mergers, focusing on serendipitous detections in the Wide-Fast-Deep (WFD) survey. We simulate observations of kNe with proposed LSST survey strategies, paying particular attention to cadence choices that are compatible with the broader LSST cosmology programme. We find that if all kNe are identical to GW170817, the baseline survey strategy will yield 58 kNe over the survey lifetime. If we instead assume a representative population model of BNS kNe, we expect to detect only 27 kNe. However, we find the choice of survey strategy significantly impacts these numbers and can increase them to 254 kNe and 82 kNe over the survey lifetime, respectively. This improvement arises from an increased cadence of observations between different filters with respect to the baseline. We then consider the ability of the Advanced LIGO/Virgo (ALV) detector network to detect these BNS mergers. If the optimal survey strategy is adopted, 202 of the GW170817-like kNe and 56 of the BNS population model kNe are detected with LSST but are below the threshold for detection by the ALV network. This represents, for both models, an increase by a factor greater than 4.5 in the number of detected sub-threshold events over the baseline survey strategy. Such a population of sub-threshold events would provide an opportunity to conduct electromagnetic-triggered searches for signals in gravitational-wave detector data and assess selection effects in measurements of the Hubble constant from standard sirens, e.g., related to viewing angle effects.
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