Early and accurate identification of strongly lensed Type Ia supernovae (SNe Ia) is essential for advancing cosmological studies, particularly in the era of the Legacy Survey of Space and Time (LSST). Conventional classifiers, such as recurrent neural networks (RNNs) and convolutional neural networks (CNNs), typically require interpolation to regularize irregularly sampled, sparse light curves, which can introduce biases and limit online applicability. We leverage Neural Controlled Differential Equations (NCDEs) to naturally model supernova light curves as continuous-time processes. NCDEs natively handle missing data and uneven sampling without interpolation, allowing full-light-curve training and seamless online classification: as new photometric points arrive (e.g., nightly LSST updates), predictions can be refreshed at any epoch without retraining or truncation. To further improve detection of multiple lensed images in the same host galaxy, we fuse NCDE outputs with transformer-based encoders that jointly attend to all available light curves. Our framework will be trained and evaluated on Phase 1 of the JOLTEON dataset — a realistic, simulated extension of the ELASTICC transient challenge that incorporates both strongly lensed SNe Ia and core-collapse supernovae — providing LSST-like sampling patterns and noise characteristics. Participation in the JOLTEON challenge (https://portal.nersc.gov/cfs/lsst/jolteon/) will benchmark our method against current state-of-the-art approaches and inform optimizations ahead of LSST commissioning.