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Strong lensed quasi-stellar objects (QSOs) are valuable probes of theuniverse in numerous aspects. Two of these applications, reverberation mappingand measuring time delays for determining cosmological parameters, require thesource QSOs to be variable with sufficient amplitude. In this paper, weforecast the number of strong lensed QSOs with sufficient variability to bedetected by the Vera C. Rubin Telescope Legacy Survey of Space and Time (LSST).The damped random walk model is employed to model the variability amplitude oflensed QSOs taken from a mock catalog by Oguri & Marshall (2010). We expect30--40% of the mock lensed QSO sample, which corresponds to $\sim$1000, toexhibit variability detectable with LSST. A smaller subsample of 250 lensedQSOs will show larger variability of $>0.15$~mag for bright lensed images with$i<21$ mag, allowing for monitoring with smaller telescopes. We discusssystematic uncertainties in the prediction by considering alternativeprescriptions for variability and mock lens catalog with respect to ourfiducial model. Our study shows that a large-scale survey of lensed QSOs can beconducted for reverberation mapping and time delay measurements following up onLSST.

Strong Lensed QSOs with Variability Detectable by LSST: How many are there?