Can we discern millilensed gravitational-wave signals from signals produced by precessing binary black holes with ground-based detectors?

Millilensed gravitational waves (GWs) can potentially be identified by the interference signatures caused by $\sim\!O(10\textrm{--}100)~\textrm{ms}$ time delays between multiple overlapping lensed signals. However, distinguishing millilensed GWs from GWs generated by precessing binary black-hole mergers can be challenging due to their apparent similar waveform shapes. This morphological similarity may be an obstacle to template-based searches to correctly identifying the origin of observed GWs and poses a fundamental question, can we discern millilensed GW signals from signals produced by precessing binary black holes? In this study, we investigate the feasibility of distinguishing between these GWs by performing a proof-of-principle injection study of simulated millilensed precessing GW signals, within the context of ground-based LIGO-Virgo-KAGRA detector network detections. Our findings indicate that it is possible to differentiate between the two effects by comparing signal-to-noise ratios (SNRs) computed using templates based on different hypotheses for the target signal. We further show from the parameter estimation study that while lensing magnification is sensitive to precession, it is possible to identify millilensing in precessing GW signals with an SNR of 18. The recovery of precession in the presence of lensing is more challenging but improves significantly for signals with an SNR of 40. Nonetheless, neglecting millilensing effects results in biases in the recovered spins, revealing the importance of accounting for these effects in accurate GW signal analysis.