  The nature of GW190425, a presumed binary neutron star (BNS) merger detected
by the LIGO/Virgo Scientific Collaboration (LVC) with a total mass of
$3.4^{+0.3}_{-0.1}$ M$_{\odot}$, remains a mystery. With such a large total
mass, GW190425 stands at five standard deviations away from the total mass
distribution of Galactic BNSs of $2.66\pm 0.12$ M$_{\odot}$. LVC suggested that
this system could be a BNS formed from a fast-merging channel rendering its
non-detection at radio wavelengths due to selection effects. BNSs with orbital
periods less than a few hours - progenitors of LIGO/Virgo mergers - are prime
target candidates for the future Laser Interferometer Space Antenna (LISA). If
GW190425-like binaries exist in the Milky Way, LISA will detect them within the
volume of our Galaxy and will measure their chirp masses to better than 10% for
those binaries with gravitational wave frequencies larger than 2 mHz. This work
explores how we can probe a population of Galactic GW190425-like BNSs with LISA
and investigate their origin. We assume that the Milky Way's BNS population
consists of two distinct sub-populations: a fraction $w_1$ that follows the
observed Galactic BNS chirp mass distribution and $w_2$ that resembles chirp
mass of GW190425. We show that LISA's accuracy on recovering the fraction of
GW190425-like binaries depends on the BNS merger rate. For the merger rates
reported in the literature, $21 - 212\,$Myr$^{-1}$, the error on the recovered
fractions varies between $\sim 30 - 5$%.
