  We report the discovery of ZTF J0127+5258, a compact mass-transferring binary
with an orbital period of 13.7 minutes. The system contains a white dwarf
accretor, which likely originated as a post-common envelope carbon-oxygen (CO)
white dwarf, and a warm donor ($T_{\rm eff,\,donor}= 16,400\pm1000\,\rm K$).
The donor probably formed during a common envelope phase between the CO white
dwarf and an evolving giant which left behind a helium star or helium white
dwarf in a close orbit with the CO white dwarf. We measure gravitational
wave-driven orbital inspiral with $\sim 35\sigma$ significance, which yields a
joint constraint on the component masses and mass transfer rate. While the
accretion disk in the system is dominated by ionized helium emission, the donor
exhibits a mixture of hydrogen and helium absorption lines. Phase-resolved
spectroscopy yields a donor radial-velocity semi-amplitude of $771\pm27\,\rm
km\, s^{-1}$, and high-speed photometry reveals that the system is eclipsing.
We detect a {\it Chandra} X-ray counterpart with $L_{X}\sim 3\times
10^{31}\,\rm erg\,s^{-1}$. Depending on the mass-transfer rate, the system will
likely evolve into either a stably mass-transferring helium CV, merge to become
an R Crb star, or explode as a Type Ia supernova in the next million years. We
predict that the Laser Space Interferometer Antenna (LISA) will detect the
source with a signal-to-noise ratio of $24\pm6$ after 4 years of observations.
The system is the first \emph{LISA}-loud mass-transferring binary with an
intrinsically luminous donor, a class of sources that provide the opportunity
to leverage the synergy between optical and infrared time domain surveys, X-ray
facilities, and gravitational-wave observatories to probe general relativity,
accretion physics, and binary evolution.
