  The upcoming Large Synoptic Survey Telescope (LSST) will detect many strongly
lensed Type Ia supernovae (LSNe Ia) for time-delay cosmography. This will
provide an independent and direct way for measuring the Hubble constant $H_0$,
which is necessary to address the current $4.4 \sigma$ tension in $H_0$ between
the local distance ladder and the early Universe measurements. We present a
detailed analysis of different observing strategies for the LSST, and quantify
their impact on time-delay measurement between multiple images of LSNe Ia. For
this, we produced microlensed mock-LSST light curves for which we estimated the
time delay between different images. We find that using only LSST data for
time-delay cosmography is not ideal. Instead, we advocate using LSST as a
discovery machine for LSNe Ia, enabling time delay measurements from follow-up
observations from other instruments in order to increase the number of systems
by a factor of 2 to 16 depending on the observing strategy. Furthermore, we
find that LSST observing strategies, which provide a good sampling frequency
(the mean inter-night gap is around two days) and high cumulative season length
(ten seasons with a season length of around 170 days per season), are favored.
Rolling cadences subdivide the survey and focus on different parts in different
years; these observing strategies trade the number of seasons for better
sampling frequency. In our investigation, this leads to half the number of
systems in comparison to the best observing strategy. Therefore rolling
cadences are disfavored because the gain from the increased sampling frequency
cannot compensate for the shortened cumulative season length. We anticipate
that the sample of lensed SNe Ia from our preferred LSST cadence strategies
with rapid follow-up observations would yield an independent percent-level
constraint on $H_0$.
