We examine the dust geometry and Ly{alpha} scattering in the galaxies of the Lyman Alpha Reference Sample (LARS), a set of 14 nearby (0.02 < $z$ < 0.2) Ly{alpha} emitting and starbursting systems with Hubble Space Telescope Ly{alpha}, H{alpha}, and H{beta} imaging. We find that the global dust properties determined by line ratios are consistent with other studies, with some of the LARS galaxies exhibiting clumpy dust media while others of them show significantly lower Ly{alpha} emission compared to their Balmer decrement. With the LARS imaging, we present Ly{alpha}/H{alpha} and H{alpha}/H{beta} maps with spatial resolutions as low as $sim$ 40 pc, and use these data to show that in most galaxies, the dust geometry is best modeled by three distinct regions: a central core where dust acts as a screen, an annulus where dust is distributed in clumps, and an outer envelope where Ly{alpha} photons only scatter. We show that the dust that affects the escape of Ly{alpha} is more restricted to the galaxies central regions, while the larger Ly{alpha} halos are generated by scattering at large radii. We present an empirical modeling technique to quantify how much Ly{alpha} scatters in the halo, and find that this characteristic scattering distance correlates with the measured size of the Ly{alpha} halo. We note that there exists a slight anti-correlation between the scattering distance of Ly{alpha} and global dust properties.
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