Resolving dust and Ly{\alpha} emission in a lensed galaxy at the epoch of reionization with JWST/CANUCS
Lyman $\alpha$ emission is highly sensitive to dust and neutral hydrogen and is therefore expected to be strongly suppressed in dusty or gas-rich galaxies during the epoch of reionization (EoR). Nevertheless, numerous moderately dusty Ly$\alpha$ emitters (LAEs) are observed at this epoch, suggesting that complex interstellar medium (ISM) geometries and feedback-driven outflows may facilitate Ly$\alpha$ escape. We investigate the dust, gas, and stellar properties of the gravitationally lensed LAE HCM 6A at $z=6.5676$ to characterize its multiphase ISM and the physical conditions regulating Ly$\alpha$ escape. We combine JWST/NIRISS slitless spectroscopy, HST+JWST/NIRCam imaging, and JWST/NIRSpec slit spectra from the CANUCS program. Using a customized BAGPIPES SED-fitting framework with a flexible attenuation law, we derive stellar, nebular, and dust properties on integrated ($\sim$kpc), slit-level ($\sim$0.1 kpc), and pixel-level ($\sim$25 pc) scales, enabled by strong lensing ($\mu \approx 8.3$-$9.1$). A Ly$\alpha$ map from SLEUTH traces the spatial distribution of Ly$\alpha$ emission. We measure an unlensed stellar mass of $\log M_\ast = 8.3$-$8.4$ and an intrinsic UV magnitude of $M_{\rm UV} = -19.8 \pm 0.1$. The older region (S1) is moderately dusty with consistent stellar and nebular attenuation indicators, implying a uniform ISM geometry, while the youngest region (S3) shows strong discrepancies among dust tracers, indicating a feedback-shaped multiphase ISM. Ly$\alpha$ emission arises primarily from S3, where a dust-cleared central clump enables efficient Ly$\alpha$ escape. We find Calzetti-like attenuation curves with a UV bump that strengthens with stellar age and decreasing $A_V$. Our observations provide a uniquely detailed, spatially resolved view of a moderately dusty LAE during the EoR, demonstrating how feedback and multiphase ISM structure govern Ly$\alpha$ escape.