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Abstract Lyαline profiles are a powerful probe of interstellar medium (ISM) structure, outflow speed, and Lyman-continuum escape fraction. In this paper, we present the Lyαline profiles of the Cosmic Origins Spectrograph (COS) Legacy Archive Spectroscopic SurveY, a sample rich in spectroscopic analogs of reionization-era galaxies. A large fraction of the spectra show a complex profile, consisting of a double-peaked Lyαemission profile in the bottom of a damped, Lyαabsorption trough. Such profiles reveal an inhomogeneous ISM. We successfully fit the damped Lyαabsorption and the Lyαemission profiles separately, but with complementary covering factors, a surprising result because this approach requires no Lyαexchange between high-N_Hiand low-N_Hipaths. The combined distribution of column densities is qualitatively similar to the bimodal distributions observed in numerical simulations. We find an inverse relation between Lyαpeak separation and the [Oiii]/[Oii] flux ratio, confirming that the covering fraction of Lyman-continuum-thin sightlines increases as the Lyαpeak separation decreases. We combine measurements of Lyαpeak separation and Lyαred peak asymmetry in a diagnostic diagram, which identifies six Lyman-continuum leakers in the COS Legacy Archive Spectrocopy SurveY (CLASSY) sample. We find a strong correlation between the Lyαtrough velocity and the outflow velocity measured from interstellar absorption lines. We argue that greater vignetting of the blueshifted Lyαpeak, relative to the redshifted peak, is the source of the well-known discrepancy between shell-model parameters and directly measured outflow properties. The CLASSY sample illustrates how scattering of Lyαphotons outside the spectroscopic aperture reshapes Lyαprofiles because the distances to these compact starbursts span a large range.