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The observed properties of the Lyman-α (Ly α) emission line are a powerful probe of neutral gas in and around galaxies. We present spatially resolved Ly α spectroscopy with VLT/MUSE targeting VR7, a UV-luminous galaxy at z = 6.532 with moderate Ly α equivalent width (EW0 ≈ 38 Å). These data are combined with deep resolved [CII]158μm spectroscopy obtained with ALMA and UV imaging from HST and we also detect UV continuum with MUSE. Ly α emission is clearly detected with S/N ≈ 40 and FWHM of 374 km s−1. Ly α and [C ii] are similarly extended beyond the UV, with effective radius reff = 2.1 ± 0.2 kpc for a single exponential model or r$_{\rm eff, Ly\alpha , halo} = 3.45^{+1.08}_{-0.87}$ kpc when measured jointly with the UV continuum. The Ly α profile is broader and redshifted with respect to the [C ii] line (by 213 km s−1), but there are spatial variations that are qualitatively similar in both lines and coincide with resolved UV components. This suggests that the emission originates from two components with plausibly different H i column densities. We place VR7 in the context of other galaxies at similar and lower redshift. The Ly α halo scale length is similar at different redshifts and velocity shifts with respect to the systemic are typically smaller. Overall, we find little indications of a more neutral vicinity at higher redshift. This means that the local (∼10 kpc) neutral gas conditions that determine the observed Ly α properties in VR7 resemble the conditions in post-reionization galaxies.