Gravitationally lensed Type Ia supernovae (SNe Ia) may be the next frontier in cosmic probes, able to deliver independent constraints on dark energy, spatial curvature, and the Hubble constant. Measurements of time delays between the multiple images become more incisive due to the standardized candle nature of the source, monitoring for months rather than years, and partial immunity to microlensing. While currently extremely rare, hundreds of such systems should be detected by upcoming time domain surveys. Others will have the images spatially unresolved, with the observed lightcurve a superposition of time-delayed image fluxes. We investigate whether unresolved images can be recognized as lensed sources given only lightcurve information, and whether time delays can be extracted robustly. We develop a method that we show can identify these systems for the case of lensed SNe Ia with two images and time delays exceeding ten days. When tested on such an ensemble, without microlensing, the method achieves a false-positive rate of <5%, and measures the time delays with a completeness of > 93% and with a bias of <0.5% for Δt > 10 days. Since the method does not assume a template of any particular type of SN, the method has the (untested) potential to work on other types of lensed SNe systems and possibly on other transients as well.