We report on a study to determine the efficiency of the Large Synoptic Survey Telescope to recover the periods and shapes of RR Lyrae light curves, and their brightnesses. We select the smoothed light curves of 40 such stars observed by the SDSS in the "Stripe 82" region, 30 of type RRab and 10 of type RRc, that evenly sample the known period-shape relationship for these stars. We place each of these in 1007 fields across the sky, each of which represents a different realization of the LSST sampling cadence. A light curve simulation tool was used to sample the light curves, returning each as it would have been observed by LSST, including realistic limiting magnitudes and photometric scatter. We report here the brightness, period, and Fourier-shape recovery as a function of distance from ~ 75 kpc to ~ 2 Mpc, with survey lengths varying from one to ten years. We find that ten years of LSST data are sufficient to recover the pulsation periods with a precision exceeding 0.001% for ~ 90% of stars within ~ 380 kpc of the Sun for Universal Cadence (UC) fields, and out to ~ 760 kpc for Deep Drilling (DD) fields, with the limit for successful period recoveries extending out to ~ 1.5 Mpc. For virtually all stars that had their periods recovered, their Fourier-based light curve shape parameter phi-31 was recovered with sufficient precision to recover photometric metallicities to within 0.14 dex out to ~ 1 Mpc in both the UC and DD fields.