  We report the detection of extended Lyman-$\alpha$ emission from the host
galaxy of SDSS~J2222+2745, a strongly lensed quasar at $z = 2.8$. Spectroscopic
follow-up clearly reveals extended Lyman-$\alpha$ in emission between two
images of the central active galactic nucleus (AGN). We reconstruct the lensed
quasar host galaxy in the source plane by applying a strong lens model to HST
imaging, and resolve spatial scales as small as $\sim$200 parsecs. In the
source plane we recover the host galaxy morphology to within a few hundred
parsecs of the central AGN, and map the extended Lyman-$\alpha$ emission to its
physical origin on one side of the host galaxy at radii $\sim$0.5-2 kpc from
the central AGN. There are clear morphological differences between the
Lyman-$\alpha$ and rest-frame ultraviolet stellar continuum emission from the
quasar host galaxy. Furthermore, the relative velocity profiles of quasar
Lyman-$\alpha$, host galaxy Lyman-$\alpha$, and metal lines in outflowing gas
reveal differences in the absorbing material affecting the AGN and host galaxy.
These data indicate the presence of patchy local intervening gas in front of
the central quasar and its host galaxy. This interpretation is consistent with
the central luminous quasar being obscured across a substantial fraction of its
surrounding solid angle, resulting in strong anisotropy in the exposure of the
host galaxy to ionizing radiation from the AGN. This work demonstrates the
power of strong lensing-assisted studies to probe spatial scales that are
currently inaccessible by other means.
