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We use the astraeus framework to investigate how the visibility and spatial distribution of Lyman-α (Lyα) emitters (LAEs) during reionization is sensitive to a halo mass-dependent fraction of ionizing radiation escaping from the galactic environment (f esc) and the ionization topology. To this end, we consider the two physically plausible bracketing scenarios of f esc increasing and decreasing with rising halo mass. We derive the corresponding observed Lyα luminosities of galaxies for three different analytic Lyα line profiles and associated Lyα escape fraction (⁠|$f_\mathrm{esc}^\mathrm{Ly\alpha }$|⁠) models: importantly, we introduce two novel analytic Lyα line profile models that describe the surrounding interstellar medium (ISM) as dusty gas clumps. They are based on parameterizing results from radiative transfer simulations, with one of them relating |$f_\mathrm{esc}^\mathrm{Ly\alpha }$| to f esc by assuming the ISM of being interspersed with low-density tunnels. Our key findings are: (i) for dusty gas clumps, the Lyα line profile develops from a central to double peak dominated profile as a galaxy's halo mass increases; (ii) LAEs are galaxies with |$M_h\gtrsim 10^{10}\, {\rm \rm M_\odot }$| located in overdense and highly ionized regions; (iii) for this reason, the spatial distribution of LAEs is primarily sensitive to the global ionization fraction and only weakly in second-order to the ionization topology or a halo mass-dependent f esc; (iv) furthermore, as the observed Lyα luminosity functions reflect the Lyα emission from more massive galaxies, there is a degeneracy between the f esc-dependent intrinsic Lyα luminosity and the Lyα attenuation by dust in the ISM if f esc does not exceed |$\sim 50~{{\ \rm per \, cent}}$|⁠. [ABSTRACT FROM AUTHOR]