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Strongly-lensed supernovae are rare and valuable probes of cosmology andastrophysics. Upcoming wide-field time-domain surveys, such as the Vera C.Rubin Observatory's Legacy Survey of Space and Time (LSST), are expected todiscover an order-of-magnitude more lensed supernovae than have previously beenobserved. In this work, we investigate the cosmological prospects of lensedtype Ia supernovae (SNIa) in LSST by quantifying the expected annual number ofdetections, the impact of stellar microlensing, follow-up feasibility, and howto best separate lensed and unlensed SNIa. We simulate SNIa lensed by galaxies,using the current LSST baseline v3.0 cadence, and find an expected number of 44lensed SNIa detections per year. Microlensing effects by stars in the lensgalaxy are predicted to lower the lensed SNIa detections by $\sim 8 \%$. Thelensed events can be separated from the unlensed ones by jointly consideringtheir colours and peak magnitudes. We define a `gold sample' of $\sim 10$lensed SNIa per year with time delay $> 10$ days, $> 5$ detections beforelight-curve peak, and sufficiently bright ($m_i < 22.5$ mag) for follow-upobservations. In three years of LSST operations, such a sample is expected toyield a $1.5\%$ measurement of the Hubble constant.

Detecting strongly-lensed type Ia supernovae with LSST