  We estimate the properties of the double neutron star (DNS) population that
will be observable by the planned space-based interferometer LISA. By following
the gravitational radiation driven evolution of DNSs generated from rapid
population synthesis of massive binary stars, we estimate that around 35 DNSs
will accumulate a signal-to-noise ratio above 8 over a four-year LISA mission.
The observed population mainly comprises Galactic DNSs (94 per cent), but
detections in the LMC (5 per cent) and SMC (1 per cent) may also be expected.
The median orbital frequency of detected DNSs is expected to be 0.8 mHz, and
many of them will be eccentric (median eccentricity of $0.11$). The orbital
properties will provide insights into DNS progenitors and formation channels.
LISA is expected to localise these DNSs to a typical angular resolution of
$2^\circ$, with best-constrained sources localised to a few arcminutes. These
localisations may allow neutron star natal kick magnitudes to be constrained
through the Galactic distribution of DNSs, and make it possible to follow up
the sources with radio pulsar searches. However, LISA is also expected to
resolve $\sim 10^4$ Galactic double white dwarfs, many of which may have binary
parameters that resemble DNSs; we discuss how the combined measurement of
binary eccentricity, chirp mass, and sky location may aid the identification of
a DNS. We expect the best-constrained DNSs to have eccentricities known to a
few parts in a thousand, chirp masses measured to better than 1 per cent
fractional uncertainty, and sky localisation at the level of a few arcminutes.
