  Neutron star$-$white dwarf (NSWD) binaries are one of the most abundant
sources of gravitational waves (GW) in the Milky Way. These GW sources are the
evolutionary products of primordial binaries that experienced many processes of
binary interaction. We employ a binary population synthesis method to
investigate the properties of Galactic NSWD binaries detectable by the Laser
Interferometer Space Antenna (LISA). In this paper, only the NSWD systems with
a COWD or ONeWD component are included. We consider various models related to
mass transfer efficiencies during primordial binary evolution, supernova
explosion mechanisms at NS formation, common envelope ejection efficiencies,
and critical WD masses that determining the stability of mass transfer between
WDs and NSs. Based on our calculations, we estimate that tens to hundreds of
LISA NSWD binaries exist in the Milky Way. We find that the detection of LISA
NSWD binaries is able to provide profound insights into mass transfer
efficiencies during the evolution of primordial binaries and critical WD masses
during mass transfer from a WD to an NS.
