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⊙, 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 ± 0.12 M⊙. 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 per cent 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 subpopulations: a fraction w1 that follows the observed Galactic BNS chirp mass distribution and w2 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 ∼30 and 5 per cent.