  Observations of binaries containing pairs of neutron stars using the upcoming
space-based gravitational wave observatory, LISA, have the potential to improve
our understanding of neutron star physics and binary evolution. In this work we
assess the effect of changing the model of the Milky Way's kinematics and star
formation history on predictions of the population of double neutron stars that
will be detected and resolved by LISA. We conclude that the spatial
distribution of these binaries is insensitive to the choice of galactic models,
compared to the stochastic variation induced by the small sample size. In
particular, the time-consuming computation of the binaries' Galactic orbits is
not necessary. The distributions of eccentricity and gravitational-wave
frequency are, however, affected by the choice of star-formation history.
Binaries with eccentricities e>0.1, which can be measured by LISA observations,
are mostly younger than 100 Myr. We caution that comparisons between different
predictions for LISA observations need to use consistent star formation
histories, and that the Galactic star formation history should be taken into
account in the analysis of the observations themselves. The lack of strong
dependency on Galactic models means that LISA detection of double neutron star
binaries may provide a relatively clean probe of massive binary star evolution.
