The revolutionary power of future Rubin-LSST observations will allow us to significantly improve the physics of pulsating stars, including RR Lyrae. In this context, an updated theoretical scenario predicting all the relevant pulsation observables in the corresponding photometric filters is mandatory. The bolometric light curves are based on a recently computed extensive set of nonlinear convective pulsation models for RR Lyrae stars, covering a broad range of metal content, and have been transformed into the Vera C. Rubin Observatory Legacy Survey of Space and Time (Rubin-LSST) photometric system. Predicted Rubin-LSST mean magnitudes and pulsation amplitudes have been adopted to build the Bailey diagrams (luminosity amplitude versus period) and the color-color diagrams in these bands. The current findings indicate that the g LSST-r LSST and r LSST-i LSST colors obey to a well-defined linear relation with the metal content. Moreover, the period-luminosity relations display in the reddest filters (r LSST, i LSST, z LSST, y LSST) a significant dependence on the assumed metal abundance. In particular, more metal-rich RR Lyrae are predicted to be fainter at a fixed period. Metal-dependent period-Wesenheit relations for different combinations of optical and near-infrared filters are also provided. These represent powerful tools to infer individual distances independently of reddening uncertainties, once the metal abundance is known and no relevant deviations from the adopted extinction law occur. Finally, we also derived new linear and quadratic absolute magnitude metallicity relations (g LSST versus [Fe/H]) and the metallicity coefficient is consistent with previous findings concerning the B and the V band.