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Context.TheVera RubinObservatory will provide an unprecedented set of time-dependent observations of the sky. The planned Legacy Survey of Space and Time (LSST), operating for ten years, will provide dense light curves for thousands of active galactic nuclei (AGN) in deep drilling fields (DDFs) and less dense light curves for millions of AGN from the main survey (MS). Aims.We model the prospects for measuring the time delays for the AGN emission lines with respect to the continuum, using these data. Methods.We modeled the artificial light curves using the Timmer-König algorithm. We used the exemplary cadence to sample them (one for the MS and one for the DDF), we supplement light curves with the expected contamination by the strong emission lines (Hβ, Mg II, and CIV, as well as with Fe II pseudo-continuum and the starlight). We chose suitable photometric bands that are appropriate for the redshift and compared the assumed line time-delay with the recovered time delay for 100 statistical realizations of the light curves. Results.We show that time delays for emission lines can be well measured from the main survey for the bright tail of the quasar distribution (about 15% of all sources) with an accuracy within 1σerror. For the DDF, the results for fainter quasars are also reliable when the entire ten years of data are used. There are also some prospects to measure the time delays for the faintest quasars at the lowest redshifts from the first two years of data, and possibly even from the first season. The entire quasar population will allow us to obtain results of apparently high accuracy, but in our simulations, we see a systematic offset between the assumed and recovered time delay that depends on the redshift and source luminosity. This offset will not disappear even in the case of large statistics. This problem might affect the slope of the radius-luminosity relation and cosmological applications of quasars if no simulations are performed that correct for these effects.