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Gravitationally lensed supernovae (glSNe) are of interest for time delaycosmology and SN physics. However, glSNe detections are rare, owing to theintrinsic rarity of SN explosions, the necessity of alignment with a foregroundlens, and the relatively short window of detectability. We present the LasCumbres Observatory Lensed Supernova Search, LCOLSS, a targeted survey designedfor detecting glSNe in known strong-lensing systems. Using cadenced$r^\prime$-band imaging, LCOLSS targeted 112 galaxy-galaxy lensing systems withhigh expected SN rates, based on estimated star formation rates. No plausibleglSN was detected by LCOLSS over two years of observing. The analysis performedhere measures a detection efficiency for these observations and runs a MonteCarlo simulation using the predicted supernova rates to determine the expectednumber of glSN detections. The results of the simulation suggest an expectednumber 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, TypeIa, and core-collapse (CC) SNe respectively. These results are broadlyconsistent with the absence of a detection in our survey. Analysis of thesurvey strategy can provide insights for future efforts to develop targetedglSN discovery programs. We thereby forecast expected detection rates for theRubin observatory for such a targeted survey, finding that a single visit depthof 24.7 mag with the Rubin observatory will detect $0.63 \pm 0.38$ SNe peryear, with $0.47 \pm 0.28$ core collapse SNe per year and $0.16 \pm 0.10$ TypeIa SNe per year.

A targeted search for strongly lensed supernovae and expectations for targeted searches in the Rubin era