  Neutron star-white dwarf (NS+WD) binaries offer a unique opportunity for
studying NS-specific phenomena with gravitational waves. In this paper, we
employ the binary population synthesis technique to study the Galactic
population of NS+WDs with the future Laser Interferometer Space Antenna (LISA).
We anticipate approximately $\mathcal{O}(10^2)$ detectable NS+WDs by LISA,
encompassing both circular and eccentric binaries formed via different
pathways. Despite the challenge of distinguishing NS+WDs from more prevalent
double white dwarfs in the LISA data (especially at frequencies below 2 mHz),
we show that their eccentricity and chirp mass distributions may provide
avenues to explore the NS natal kicks and common envelope evolution.
Additionally, we investigate the spatial distribution of detectable NS+WDs
relative to the Galactic plane and discuss prospects for identifying
electromagnetic counterparts at radio wavelengths. Our results emphasise LISA's
capability to detect and characterise NS+WDs and to offer insights into the
properties of the underlying population. Our conclusions carry significant
implications for shaping LISA data analysis strategies and future data
interpretation.
