We present a framework to study the orientation distribution of nearby double white dwarf binaries with LISA, explicitly accounting for the fourfold degeneracy in the polarization angle. Exploiting the beltlike sky distribution of the nearby sample along the Galactic plane, we show that the low-multipole extraction can be recast as an effectively one-dimensional Fourier analysis along Galactic longitude, within a spherical-harmonic expansion based on the Wigner-$D$ formalism. The symmetry with respect to the Galactic plane governs the sensitivity: modes even under reflection across the plane remain accessible, while odd modes are strongly suppressed. For a fiducial sample of about 500 binaries within $\lesssim 4\mathrm{kpc}$, corresponding to roughly 5% of the resolved Galactic population, the method yields an uncertainty of order 0.02 for the reflection-even coefficients with $\ell \le 3$, and is readily applicable to the forthcoming LISA catalog.

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• Gravitational waves
• Binary stars