Can we discern microlensed gravitational-wave signals from the signal of precessing compact binary mergers?

Microlensed gravitational waves (GWs) are likely observable by recognizing the signature of interference caused by $\sim\!\mathcal{O}(10\textrm{--}100)~\textrm{ms}$ time delays between multiple lensed signals. However, the shape of the anticipated microlensed GW signals might be confused with the modulation appearing in the waveform of GWs from precessing compact binary mergers. Their morphological similarity may be an obstacle to template-based searches to correctly identifying the origin of observed GWs and it seamlessly raises a fundamental question, can we discern microlensed GW signals from the signal of precessing compact binary mergers? We discuss the feasibility of distinguishing those GWs via examining simulated GW signals with and without the presence of noise. We find that it is certainly possible if we compare signal-to-noise ratios (SNRs) computed with templates of different hypotheses for a given target signal. We show that proper parameter estimation for lensed GWs enables us to identify the targets of interest by focusing on a half number of assumptions for the target signal than the SNR-based test.