Aims. We wish to investigate the physical properties of a sample of Lyα emitting galaxies in the VANDELS survey, with particular focus on the role of kinematics and neutral hydrogen column density in the escape and spatial distribution of Lyα photons. Methods. From all the Lyα emitting galaxies in the VANDELS Data Release 2 at 3.5 ≲ z ≲ 4.5, we selected a sample of 52 galaxies that also have a precise systemic redshift determination from at least one nebular emission line (HeII or CIII]). For these galaxies, we derived different physical properties (stellar mass, age, dust extinction, and star formation rate) from spectral energy distribution (SED) fitting of the exquisite multiwavelength photometry available in the VANDELS fields, using the dedicated spectral modeling tool BEAGLE and the UV β slope from the observed photometry. We characterized the Lyα emission in terms of kinematics, equivalent width (EW), full width at half-maximum, and spatial extension and then estimated the velocity of the neutral outflowing gas. The ultra-deep VANDELS spectra (up to 80 h on-source integration) enable this for individual galaxies without the need to rely on stacks. We then investigated the correlations between the Lyα properties and the other measured properties to study how they affect the shape and intensity of Lyα emission. Results. We reproduce some of the well-known correlations between Lyα EW and stellar mass, dust extinction, and UV β slope, in the sense that the emission line appears brighter in galaxies with lower mass that are less dusty and bluer. We do not find any correlation with the SED-derived star formation rate, while we find that galaxies with brighter Lyα tend to be more compact in both UV and in Lyα. Our data reveal an interesting correlation between the Lyα velocity offset and the shift of the interstellar absorption lines with respect to the systemic redshift, observed for the first time at high redshifts: galaxies with higher interstellar medium (ISM) outflow velocities show smaller Lyα velocity shifts. We interpret this relation in the context of the shell-model scenario, where the velocity of the ISM and the HI column density contribute together in determining the Lyα kinematics. In support to our interpretation, we observe that galaxies with high HI column densities have much more extended Lyα spatial profiles; this is a sign of increased scattering. However, we do not find any evidence that the HI column density is related to any other physical properties of the galaxies, although this might be due in part to the limited range of parameters that our sample spans.