  The discovery of habitable zone (HZ) planets around low-mass stars has
highlighted the need for a comprehensive understanding of the radiation
environments in which such planets reside. Of particular importance is
knowledge of the far-ultraviolet (FUV) radiation, as low-mass stars are
typically much more active than solar-type stars and the proximity of their HZs
can be one tenth the distance. The vast majority of the flux emitted by
low-mass stars at FUV wavelengths occurs in the Lyman-$\alpha$ line at 1216
Angstroms. However, measuring a low-mass star's Lyman-$\alpha$ emission
directly is almost always impossible because of the contaminating effects of
interstellar hydrogen and geocoronal airglow. We observed Ross 825 (K3) and
Ross 1044 (M0), two stars with exceptional radial velocities, with the STIS
spectrograph aboard the Hubble Space Telescope (HST). Their radial velocities
resulted in significant line shifts, allowing for a more complete view of their
Lyman-$\alpha$ line profiles. We provide an updated relation between effective
temperature and Lyman-$\alpha$ flux using Gaia DR2 astrometry as well as
updated, model-independent relationships between Lyman-$\alpha$ flux and UV
flux measurements from the Galaxy Evolution Explorer (GALEX) for low-mass
stars. These new relations, in combination with GALEX's considerable spatial
coverage, provide substantial predictive power for the Lyman-$\alpha$
environments for thousands of nearby, low-mass stars.
