We extend a previous study of Lyman alpha emitters (LAEs) based on hydrodynamical cosmological simulations, by including two physical processes important for LAEs: (i) Lyα and continuum luminosities produced by cooling of collisionally excited H i in the galaxy and (ii) dust formation and evolution; we follow these processes on a galaxy-by-galaxy basis. H i cooling on average contributes 16–18 per cent of the Lyα radiation produced by stars, but this value can be much higher in low-mass LAEs and further increased if the H i is clumpy. The continuum luminosity is instead almost completely dominated by stellar sources. The dust content of galaxies scales with their stellar mass, Mdust∝M0.7*, and stellar metallicity, Z*, such that Mdust∝Z1.7*. As a result, the massive galaxies have Lyα escape fraction as low as fα= 0.1, with a LAE-averaged value decreasing with redshift: 〈fα〉= (0.33, 0.23) at z= (5.7, 6.6). The ultraviolet (UV) continuum escape fraction shows the opposite trend with z, possibly resulting from clumpiness evolution. The model successfully reproduces the observed Lyα and UV luminosity functions at different redshifts and the Lyα equivalent width scatter to a large degree, although the observed distribution appears to be more more extended than the predicted one. We discuss possible reasons for such tension.