  We explore and demonstrate the capabilities of LSST to study Type I
superluminous supernovae (SLSNe). We first fit the light curves of 58 known
SLSNe at z~0.1-1.6, using an analytical magnetar spin-down model implemented in
MOSFiT. We then use the posterior distributions of the magnetar and ejecta
parameters to generate thousands of synthetic SLSN light curves, and we inject
those into the OpSim to generate realistic ugrizy light curves. We define
simple, measurable metrics to quantify the detectability and utility of the
light curve, and to measure the efficiency of LSST in returning SLSN light
curves satisfying these metrics. We combine the metric efficiencies with the
volumetric rate of SLSNe to estimate the overall discovery rate of LSST, and we
find that ~10^4 SLSNe per year with >10 data points will be discovered in the
WFD survey at z<3.0, while only ~15 SLSNe per year will be discovered in each
DDF at z<4.0. To evaluate the information content in the LSST data, we refit
representative output light curves with the same model that was used to
generate them. We correlate our ability to recover magnetar and ejecta
parameters with the simple light curve metrics to evaluate the most important
metrics. We find that we can recover physical parameters to within 30% of their
true values from ~18% of WFD light curves. Light curves with measurements of
both the rise and decline in gri-bands, and those with at least fifty
observations in all bands combined, are most information rich, with ~30% of
these light curves having recoverable physical parameters to ~30% accuracy. WFD
survey strategies which increase cadence in these bands and minimize seasonal
gaps will maximize the number of scientifically useful SLSN light curves.
Finally, although the DDFs will provide more densely sampled light curves, we
expect only ~50 SLSNe with recoverable parameters in each field in the
decade-long survey.
