(Abridged) Lyman-alpha (Lya) is a dominant probe of the galaxy population at high-z. However, interpretation of data drawn from Lya alone hinges on the Lya escape fraction which, due to the complex radiative transport, may vary greatly. Here we map the Lya emission from local starburst Haro 11, a Lya emitter and the only known candidate for low-z Lyman continuum emission (LyC). To aid in the interpretation we perform a detailed multi-wavelength analysis and model the stellar population, dust distribution, ionising photon budget, and star-cluster population. We use archival X-ray observations to further constrain properties of the starburst and estimate the HI column density. The Lya morphology is found to be strongly decoupled from stellar and nebular (H-alpha) morphologies. General surface photometry finds only very slight correlation between Lya and H-halpha, E(B-V), and stellar age. Only around the central Lya-bright cluster do we find the Lya/Ha ratio at values predicted by recombination theory. The total Lya escape fraction is found to be just 3%. We compute that ~90% of the Lya photons that escape do so after undergoing multiple resonance scattering events, masking their point of origin. This leads to a largely symmetric distribution and, by increasing the distance that photons must travel to escape, decreases the escape probability significantly. While dust must ultimately be responsible for the destruction of Lya, it plays little role in governing the observed morphology, which is regulated more by ISM kinematics and geometry. We find tentative evidence for local Lya equivalent width in the immediate vicinity of star-clusters being a function of cluster age, consistent with hydrodynamic studies. We estimate the ionising photon production and further constrain the escape fraction at 900 AA to <~9% .
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