We present a Bayesian framework that enhances the identification of strongly lensed gravitational waves (GWs) by incorporating an astrophysically informed spatial constraint from the Euclid galaxy lens catalog. The core of our method is a two-step positional weighting scheme: first, GW parameter estimation is performed under a uniform sky prior to obtain the GW sky localization posterior; this posterior then reweights Euclid candidate lens galaxies, yielding an astrophysically informed multimessenger spatial constraint. This constraint refines a second round of GW parameter estimation by adjusting only lens position plausibility (not intrinsic GW parameters) and isolates lens-consistent contributions in lensing Bayes factor calculation. Comparing this Euclid-constrained spatial constraint against a uniform sky constraint within our framework reveals distinct behaviors. While the posterior estimates of the intrinsic waveform parameters show little sensitivity to this constraint change, the Bayes factor for lensing identification exhibits significant dependence on the spatial constraint. Crucially, for truly lensed event pairs, the Bayes factor systematically increases, whereas for unlensed pairs it decreases. This dual effect is vital for robust discrimination. Our analysis demonstrates that this multimessenger approach significantly improves the confidence of lensing searches. For lensed pairs, the method boosts the Bayes factor by an average factor of $\sim 10$, while effectively suppressing false positives for unlensed coincidences. This underscores the critical importance of spatial constraint specification and showcases the substantial gains achievable by synergizing gravitational-wave data with electromagnetic survey information.

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• Gravitational lenses
• Gravitational waves