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The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will detect an unprecedentedly large sample of actively accreting supermassive black holes with typical accretion disk (AD) sizes of a few light days. This brings us to face challenges in the reverberation mapping (RM) measurement of AD sizes in active galactic nuclei (AGNs) using interband continuum delays. We examine the effect of LSST cadence strategies on AD RM using our metric AGNTimeLagMetric. It accounts for redshift, cadence, the magnitude limit, and magnitude corrections for dust extinction. Running our metric on different LSST cadence strategies, we produce an atlas of the performance estimations for LSST photometric RM measurements. We provide an upper limit on the estimated number of quasars for which the AD time lag can be computed within 0<z<7 using the features of our metric. We forecast that the total counts of such objects will increase as the mean sampling rate of the survey decreases. The AD time lag measurements are expected for >1000 sources in each Deep Drilling field (DDF, 10 sq. deg) in any filter, with the redshift distribution of these sources peaking at z~1. We find the LSST observation strategies with a good cadence (~ 5 days) and a long cumulative season (~9 yr), as proposed for LSST DDF, are favored for the AD size measurement. We create synthetic LSST light curves for the most suitable DDF cadences and determine RM time lags to demonstrate the impact of the best cadences based on the proposed metric.