The Ly\(\alpha\) emission line is one of the main observables of galaxies at high redshift, but its output depends strongly on the neutral gas distribution and kinematics around the star-forming regions where UV photons are produced. We present observations of Ly\(\alpha\) and 21-cm HI emission at comparable scales with the goal to qualitatively investigate how the neutral interstellar medium (ISM) properties impact Ly\(\alpha\) transfer in galaxies. We have observed 21-cm HI at the highest angular resolution possible (~ 3" beam) with the VLA in two local galaxies from the Lyman Alpha Reference Sample. We contrast this data with HST Ly\(\alpha\) imaging and spectroscopy, and MUSE and PMAS ionized gas observations. In LARS08, high intensity Ly\(\alpha\) emission is co-spatial with high column density HI where dust content is the lowest. The Ly\(\alpha\) line is strongly redshifted, consistent with velocity redistribution which allows Ly\(\alpha\) escape from high column density neutral medium with low dust content. In eLARS01, high intensity Ly\(\alpha\) emission is located in regions of low column density HI, below the HI data sensitivity limit (\(<2\times10^{20}\,\)cm\(^{-2}\)). The perturbed ISM distribution with low column density gas in front of the Ly\(\alpha\) emission region plays an important role in the escape. In both galaxies, the faint Ly\(\alpha\) emission (\(\sim 1\times10^{-16}\)erg.s\(^{-1}\)cm\(^{-2}\)arcsec\(^{-2}\)) traces intermediate H\(\alpha\) emission regions where HI is found, regardless of the dust content. Dust seems to modulate, but not prevent, the formation of a faint Ly\(\alpha\) halo. This study suggests the existence of scaling relations between dust, H\(\alpha\), HI, and Ly\(\alpha\) emission in galaxies.