  Using our 3D Lya radiation transfer code, we compute the radiation transfer
of Lya and UV continuum photons including dust. Observational constraints on
the neutral gas (column density, kinematics, etc.) are taken from other
analysis of this object. RESULTS: The observed Lya profile of MS 1512--cB58 is
reproduced for the first time taking radiation transfer and all observational
constraints into account. The observed absorption profile is found to result
naturally from the observed amount of dust and the relatively high HI column
density. Radiation transfer effects and suppresion by dust transform a strong
intrinsic Lya emission with EW(Lya)>~ 60 Ang into the observed faint superposed
Lya emission peak. We propose that the vast majority of LBGs have intrinsically
EW(Lya)~60-80 Ang or larger, and that the main physical parameter responsible
for the observed variety of Lya strengths and profiles in LBGs is N_H and the
accompanying variation of the dust content. Observed EW(Lya) distributions, Lya
luminosity functions, and related quantities must therefore be corrected for
radiation transfer and dust effects. The implications from our scenario on the
duty-cycle of Lya emitters are also discussed.
