  Aims: We aim to study the effects of an inhomogeneous interstellar medium
(ISM) on the strength and the shape of the Lyman alpha (Lya) line in starburst
galaxies. Methods: Using our 3D Monte Carlo Lya radiation transfer code, we
study the radiative transfer of Lya, UV and optical continuum photons in
homogeneous and clumpy shells of neutral hydrogen and dust surrounding a
central source. Our simulations predict the Lya and continuum escape fraction,
the Lya equivalent width EW(Lya), the Lya line profile and their dependence on
the gas geometry and the main input physical parameters. Results: The ISM
clumpiness is found to have a strong impact on the Lya line radiative transfer,
entailing a strong dependence of the emergent features of the Lya line (escape
fraction, EW(Lya)) on the ISM morphology. Although a clumpy and dusty ISM
appears more transparent to radiation (both line and continuum) compared to an
equivalent homogeneous ISM of equal dust optical depth, we find that the Lya
photons are, in general, still more attenuated than UV continuum radiation. As
a consequence, the observed Lya equivalent width (EWobs(Lya)) is lower than the
intrinsic one (EWint(Lya)) for nearly all clumpy ISM configurations considered.
There are, however, special conditions under which Lya photons escape more
easily than the continuum, resulting in an enhanced EWobs(Lya). The requirement
for this to happen is that the ISM is almost static (galactic outflows < 200
km/s), extremely clumpy (with density contrasts >10^7 in HI between clumps and
the interclump medium), and very dusty (E(B-V) > 0.30). When these conditions
are fulfilled the emergent Lya line profile shows no velocity shift and little
asymmetry. Given the asymmetry and velocity shifts generally observed in
starburst galaxies with Lya emission, we conclude that clumping is unlikely to
significantly enhance their relative Lya/UV transmission.
