Best fit (blue solid line) obtained for the galaxy J1256+4509. The black and green solid lines show the observed flux and the error on the flux, respectively. Top panels: zooms on the individual Lyman series lines fitted. The gray shaded areas are the principal wavelength regions masked during the fit, due to geo-coronal emission, low S/N or Lyα emission. Additionally, in the top panels, we show the masks for ISM/Milky Way absorption lines that are not included during the fitting procedure. For display purposes, these masks do not appear in the main panel. The blue-shaded area represents the uncertainty on the fit, derived using a Monte-Carlo approach (see details in Sect. 3.1).