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The upcoming Large Synoptic Survey Telescope (LSST) will detect many stronglylensed Type Ia supernovae (LSNe Ia) for time-delay cosmography. This willprovide an independent and direct way for measuring the Hubble constant $H_0$,which is necessary to address the current $4.4 \sigma$ tension in $H_0$ betweenthe local distance ladder and the early Universe measurements. We present adetailed analysis of different observing strategies for the LSST, and quantifytheir impact on time-delay measurement between multiple images of LSNe Ia. Forthis, we produced microlensed mock-LSST light curves for which we estimated thetime delay between different images. We find that using only LSST data fortime-delay cosmography is not ideal. Instead, we advocate using LSST as adiscovery machine for LSNe Ia, enabling time delay measurements from follow-upobservations from other instruments in order to increase the number of systemsby a factor of 2 to 16 depending on the observing strategy. Furthermore, wefind 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 differentyears; these observing strategies trade the number of seasons for bettersampling frequency. In our investigation, this leads to half the number ofsystems in comparison to the best observing strategy. Therefore rollingcadences are disfavored because the gain from the increased sampling frequencycannot compensate for the shortened cumulative season length. We anticipatethat the sample of lensed SNe Ia from our preferred LSST cadence strategieswith rapid follow-up observations would yield an independent percent-levelconstraint on $H_0$.

Strongly lensed SNe Ia in the era of LSST: observing cadence for lens discoveries and time-delay measurements