Aims. We wish to assess the role of kinematics and neutral hydrogen column density in the escape and distribution of Lyα photons. Methods. We selected a sample of 76 Lyα emitting galaxies from the VIMOS Ultra Deep Survey (VUDS) at 2 ≤ z ≤ 4. We estimated the velocity of the neutral gas flowing out of the interstellar medium as the velocity offset, ∆v, between the systemic redshift (z sys ) and the center of low-ionization absorption line systems (LIS). To increase the signal to noise of VUDS spectra, we stacked subsamples defined based on median values of their photometric and spectroscopic properties. We measured the systemic redshift from the restframe UV spectroscopic data using the CIII]1908 nebular emission line, and we considered SiII1526 as the highest signal-to-noise LIS line. We calculated the Lyα peak shift with respect to the z sys , the EW(Lyα), and the Lyα spatial extension, Ext(Lyα-C), from the profiles in the 2D stacked spectra. Results. The galaxies that are faint in the rest-frame UV continuum, strong in Lyα and CIII], with compact UV morphology, and localized in an underdense environment are characterized by outflow velocities of the order of a few hundreds of km sec −1 . The subsamples with smaller ∆v are characterized by larger Lyα peak shifts, larger Ext(Lyα-C), and smaller EW(Lyα). In general we find that EW(Lyα) anti-correlates with Ext(LyLyα-C) and Lyα peak shift. Conclusions. We interpret these trends using a radiative-transfer shell model. The model predicts that an HI gas with a column density larger than 10 20 cm −2 is able to produce Lyα peak shifts larger than > 300 km sec −1 . An ISM with this value of N HI would favour a large amount of scattering events, especially when the medium is static, so it can explain large values of Ext(Lyα-C) and small EW(Lyα). On the contrary, an ISM with a lower N HI , but large velocity outflows would lead to a Lyα spatial profile peaked at the galaxy center (i.e. low values of Ext(Lyα-C)) and to a large EW(Lyα), as we see in our data. Our results and their interpretation via radiative-transfer models tell us that it is possible to use Lyα to study the properties of the HI gas. Also, the fact that Lyα emitters are characterized by large ∆v could give hints about their stage of evolution in the sense that they could be experiencing short bursts of star formation that push strong outflows.