  The intrinsic strength of the Ly$\alpha$ line in young, star-forming systems
makes it a special tool for studying high-redshift galaxies. However,
interpreting observations remains challenging due to the complex radiative
transfer involved. Here, we combine state-of-the-art hydrodynamical simulations
of 'Althaea', a prototypical Lyman Break Galaxy (LBG, stellar mass
$M_{\star}$$\simeq$ $10^{10}{\rm M}_{\odot})$ at $z=7.2$, with detailed
radiative transfer computations of dust/continuum, [CII] 158 $\mu$m, and
Ly$\alpha$ to clarify the relation between the galaxy properties and its
Ly$\alpha$ emission. Althaea exhibits low ($f_\alpha< 1\%$) Ly$\alpha$ escape
fractions and Equivalent Widths, EW $\lesssim 6$ Angstrom for the simulated
lines of sight, with a large scatter. The correlation between escape fraction
and inclination is weak, as a result of the rather chaotic structure of
high-redshift galaxies. Low $f_\alpha$ values persist even if we artificially
remove neutral gas around star forming regions to mimick the presence of HII
regions. The high attenuation is primarily caused by dust clumps co-located
with young stellar clusters. We can turn Althaea into a Lyman Alpha Emitter
(LAE) only if we artificially remove dust from the clumps, yielding EWs up to
$22$ Angstrom. Our study suggests that the LBG-LAE duty-cycle required by
recent clustering measurements poses the challenging problem of a dynamically
changing dust attenuation. Finally, we find an anti-correlation between the
magnitude of Ly$\alpha$-[CII] line velocity shift and Ly$\alpha$ luminosity.
