Satadru Bag, Raoul Canameras, Sherry H. Suyu, Stefan Schuldt, Stefan Taubenberger, Irham Taufik Andika, Alejandra Melo, Ming Kei Chan

Strong gravitationally lensed supernovae (LSNe) are rare but extremely valuable probes of cosmology and astrophysics. Prompt identification within the alert streams of time-domain surveys such as the Rubin Legacy Survey of Space and Time (LSST) is essential for timely follow-up observations. In our previous study, Bag et al. (2026), we introduced a deep-learning framework for detecting LSNe Ia directly from multi-band, multi-epoch image cutouts. The model employs a convolutional LSTM architecture to capture spatiotemporal correlations in time-series imaging data, enabling classification updates as new observations arrive. In this work, we extend that framework by incorporating greater realism into the simulations. In particular, we present a method to construct realistic image time series from single-epoch observations by introducing epoch-to-epoch point spread function variations with corresponding variance-map corrections. The dataset is based on HSC PDR3 observations and includes simulated lensed host-galaxy arcs, SN light-curve variations, and Poisson noise. We also introduce an additional negative class consisting of SN Ia occurring in the foreground lens galaxy, representing a challenging source of false positives. Despite these additional complexities, the model retains strong performance. The receiver operating characteristic improves rapidly during the first few observations, reaching a true-positive rate of $\sim60\%$ at a false-positive rate of $\mathcal{O}(10^{-4})$ by the seventh observation and $\sim80\%$ by the tenth. We also investigate potential confusion with sibling SNe occurring in LRGs and identify the configurations that best mimic lensed systems. These results demonstrate that the image-time-series approach remains robust under more realistic observing conditions, and is well suited for real-time LSN searches in LSST and other time-domain surveys.