  Strongly-lensed supernovae are rare and valuable probes of cosmology and
astrophysics. Upcoming wide-field time-domain surveys, such as the Vera C.
Rubin Observatory's Legacy Survey of Space and Time (LSST), are expected to
discover an order-of-magnitude more lensed supernovae than have previously been
observed. In this work, we investigate the cosmological prospects of lensed
type Ia supernovae (SNIa) in LSST by quantifying the expected annual number of
detections, the impact of stellar microlensing, follow-up feasibility, and how
to 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 44
lensed SNIa detections per year. Microlensing effects by stars in the lens
galaxy are predicted to lower the lensed SNIa detections by $\sim 8 \%$. The
lensed events can be separated from the unlensed ones by jointly considering
their colours and peak magnitudes. We define a `gold sample' of $\sim 10$
lensed SNIa per year with time delay $> 10$ days, $> 5$ detections before
light-curve peak, and sufficiently bright ($m_i < 22.5$ mag) for follow-up
observations. In three years of LSST operations, such a sample is expected to
yield a $1.5\%$ measurement of the Hubble constant.
