Results. We reproduce some of the well-known correlations between Ly alpha EW and stellar mass, dust extinction, and UV beta 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 Ly alpha tend to be more compact in both UV and in Ly alpha. Our data reveal an interesting correlation between the Ly alpha 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 Ly alpha 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 Ly alpha kinematics. In support to our interpretation, we observe that galaxies with high HI column densities have much more extended Ly alpha 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.