  The recent detections of GW150914 and GW151226 imply an abundance of
stellar-mass binary-black-hole mergers in the local universe. While
ground-based gravitational-wave detectors are limited to observing the final
moments before a binary merges, space-based detectors, such as the Laser
Interferometer Space Antenna (LISA), can observe binaries at lower orbital
frequencies where such systems may still encode information about their
formation histories. In particular, the orbital eccentricity and mass of binary
black holes in the LISA frequency band can be used together to discriminate
between binaries formed in isolation in galactic fields and those formed in
dense stellar environments such as globular clusters. In this letter, we
explore the orbital eccentricity and mass of binary-black-hole populations as
they evolve through the LISA frequency band. Overall we find that there are two
distinct populations discernible by LISA. We show that up to ~90% of binaries
formed either dynamically or in isolation have eccentricities measurable by
LISA. Finally, we note how measured eccentricities of low-mass binary black
holes evolved in isolation could provide detailed constraints on the physics of
black-hole natal kicks and common-envelope evolution.
