A targeted search for strongly lensed supernovae and expectations for
  targeted searches in the Rubin era
  Gravitationally lensed supernovae (glSNe) are of interest for time delay
cosmology and SN physics. However, glSNe detections are rare, owing to the
intrinsic rarity of SN explosions, the necessity of alignment with a foreground
lens, and the relatively short window of detectability. We present the Las
Cumbres Observatory Lensed Supernova Search, LCOLSS, a targeted survey designed
for detecting glSNe in known strong-lensing systems. Using cadenced
$r^\prime$-band imaging, LCOLSS targeted 112 galaxy-galaxy lensing systems with
high expected SN rates, based on estimated star formation rates. No plausible
glSN was detected by LCOLSS over two years of observing. The analysis performed
here measures a detection efficiency for these observations and runs a Monte
Carlo simulation using the predicted supernova rates to determine the expected
number of glSN detections. The results of the simulation suggest an expected
number of detections and $68\%$ Poisson confidence intervals, $N_{SN} = 0.20,
[0,2.1] $, $N_{Ia} = 0.08, [0,2.0]$, $N_{CC} = 0.12, [0,2.0]$, for all SN, Type
Ia, and core-collapse (CC) SNe respectively. These results are broadly
consistent with the absence of a detection in our survey. Analysis of the
survey strategy can provide insights for future efforts to develop targeted
glSN discovery programs. We thereby forecast expected detection rates for the
Rubin observatory for such a targeted survey, finding that a single visit depth
of 24.7 mag with the Rubin observatory will detect $0.63 \pm 0.38$ SNe per
year, with $0.47 \pm 0.28$ core collapse SNe per year and $0.16 \pm 0.10$ Type
Ia SNe per year.
