  The Zwicky Transient Facility (ZTF) was expected to detect more than one
strong gravitationally-lensed supernova (glSN) per year, but only one event was
identified in the first four years of the survey. This work investigates
selection biases in the search strategy that could explain the discrepancy and
revise discovery predictions. We present simulations of realistic lightcurves
for lensed thermonuclear (glSNIa) and core-collapse supernova (glCCSN)
explosions over a span of 5.33 years of the survey, utilizing the actual
observation logs of ZTF. We find that the magnitude limit in spectroscopic
screening significantly biases the selection towards highly magnified glSNe,
for which the detection rates are consistent with the identification of a
single object by ZTF. To reach the higher predicted rate of detections requires
an optimization of the identification criteria for fainter objects. We find
that around 1.36 (3.08) Type Ia SNe (CCSNe) are identifiable with the
magnification method per year in ZTF, but when applying the magnitude cut of m
< 19 mag, the detection rates decrease to 0.17 (0.32) per year. We compare our
simulations with the previously found lensed Type Ia SNe, iPTF16geu and SN
Zwicky, and conclude that considering the bias towards highly magnified events,
the findings are within expectations in terms of detection rates and lensing
properties of the systems. In addition, we provide a set of selection cuts
based on simple observables to distinguish glSNe from regular, unlensed,
supernovae to select potential candidates for spectroscopic and high-spatial
resolution follow-up campaigns. We find optimal cuts in observed colours $g-r$,
$g-i$, and $r-i$ as well as in the colour SALT2 fit parameter. The developed
pipeline and the simulated lightcurves employed in this analysis can be found
in the $LENSIT$ github repository.
