The observed properties of the Lyman-α (Lyα) emission line are a powerful probe of neutral gas in and around galaxies. We present spatially resolved Lyα spectroscopy with VLT/MUSE targeting VR7, a UV-luminous galaxy at z = 6.532 with moderate Lyα equivalent width (EW 0 = 38Å). These data are combined with deep resolved [CII] 158µm spectroscopy obtained with ALMA and UV imaging from HST. Lyα emission is clearly detected with S/N ≈ 40 and FWHM of 370 km s −1 . We also detect UV continuum with MUSE. Lyα and [CII] are similarly extended beyond the UV, with effective radius r eff = 2.1±0.2 kpc for a single component or r eff,Lyα,halo = 3.45 +1.08 −0.87 kpc when measured jointly with the UV continuum. The Lyα profile is broader and redshifted with respect to the [CII] line (by 220 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, while spatially varying HI column densities are also present. We place VR7 in the context of other galaxies at similar and lower redshift. The Lyα 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 Lyα properties in VR7 resemble the conditions in post-re-ionisation galaxies.