Abstract
Strong lensing of massive black hole binaries can produce multiple gravitational-wave images with different magnifications and arrival times. Laser Interferometer Space Antenna (LISA) signals remain in-band for months to years, allowing multiple lensed images to overlap during the inspiral stage and generate beat patterns. A singular isothermal sphere lens model was adopted to describe the lensing configuration, and two-image beat waveforms were constructed from massive black hole binary signals. To isolate the beat modulation itself, waveform mismatch was evaluated only during the overlapping inspiral stage before the coalescence of the first image, excluding contributions from the delayed merger peak of the second image. Using the strong-lensing population corresponding to the heavy-seed no-delay model with supernova feedback, HS-nod-SN (B+20), the occurrence rate of identifiable beat events was estimated, and Bayesian parameter estimation was performed with a beat template. Beat patterns are most readily identified when the lensing time delay is short and the delayed image has a relatively large magnification. Among 196 detectable two-image lensed events, 92 satisfy the temporal-overlap condition, and 14 satisfy the beat-identification criterion, corresponding to an identifiable beat fraction of about 7%. Posterior inference illustrates the parameter correlations and the broad, potentially multimodal constraint on the lensing time delay for a representative beat event. These results indicate that lensed beat patterns constitute a distinguishable subset of strongly lensed LISA events and provide a unique observational signature of strong lensing in the LISA band.