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The 1215.67A HI Lyman alpha emission line dominates the ultraviolet flux of low mass stars, including the majority of known exoplanet hosts. Unfortunately, strong attenuation by the interstellar medium (ISM) obscures the line core at most stars, requiring the intrinsic Lyman alpha flux to be reconstructed based on fits to the line wings. We present a test of the widely-used Lyman alpha emission line reconstruction code LYAPY using phase-resolved, medium-resolution STIS G140M observations of the close white dwarf-M dwarf binary EG UMa. The Doppler shifts induced by the binary orbital motion move the Lyman alpha emission line in and out of the region of strong ISM attenuation. Reconstructions to each spectrum should produce the same Lyman alpha profile regardless of phase, under the well-justified assumption that there is no intrinsic line variability between observations. Instead, we find that the reconstructions underestimate the Lyman alpha flux by almost a factor of two for the lowest-velocity, most attenuated spectrum, due to a degeneracy between the intrinsic Lyman alpha and ISM profiles. Our results imply that many stellar Lyman alpha fluxes derived from G140M spectra reported in the literature may be underestimated, with potential consequences for, for example, estimates of extreme-ultraviolet stellar spectra and ultraviolet inputs into simulations of exoplanet atmospheres.