Context. The Lyman-α (Lyα) line of hydrogen is a well-known tracer of galaxies at high redshift. However, the connection between Lyα observables and galaxy properties has not been fully established, limiting the use of the line to probe the physics of galaxies. Aims. Here, we derive the global neutral hydrogen gas (Hi) properties of nearby Lyα-emitting galaxies to assess the impact of neutral gas on the Lyα output of galaxies. Methods. We observed the 21 cm line emission using the Karl G. Jansky Very Large Array in D-array configuration (∼5500 resolution, ∼38 kpc) for 37 star-forming galaxies with available Hubble Space Telescope (HST) Lyα imaging from the Lyman Alpha Reference Samples. Results. We detected 21 cm emission for 33 out of the 37 galaxies observed. We found no significant correlation of global Hi properties (including Hi mass, column density, gas fraction, depletion time, line width, or velocity shift between Hi and Lyα), with the Lyα luminosity, escape fractions, or equivalent widths (EW) derived with HST photometry. Additionally, both Lyα-emitters and weak or non-emitters are distributed evenly along the Hi parameter space of optically selected z = 0 galaxies. Around 74% of the sample is undergoing galaxy interaction, this fraction is higher for Lyα-emitters (83% for galaxies with EW ≥ 20 Å) than for weak or non-emitters (70%). Nevertheless, galaxies identified as interacting have Lyα and Hi properties statistically consistent with those of non-interacting galaxies. Conclusions. Our results show that global Hi properties (on scales >30kpc) have little direct impact on the Lyα output from galaxies. Instead, Hi likely regulates Lyα emission on small scales: statistical comparisons of Lyα and high angular resolution 21 cm observations are required to fully assess the role of Hi in Lyα radiative transfer. While our study indicates that major and minor galaxy mergers could play a role in the emission of Lyα photons in the Local Universe, especially for galaxies with high Hi fractions, the line of sight that a system is observed through ultimately determines the Lyα observables.