  Stellar-mass black hole binaries (BHBs) near supermassive black holes (SMBH)
in galactic nuclei undergo eccentricity oscillations due to gravitational
perturbations from the SMBH. Previous works have shown that this channel can
contribute to the overall BHB merger rate detected by the Laser Interferometer
Gravitational-Wave Observatory (LIGO) and Virgo Interferometer. Significantly,
the SMBH gravitational perturbations on the binary's orbit may produce
eccentric BHBs which are expected to be visible using the upcoming Laser
Interferometer Space Antenna (LISA) for a large fraction of their lifetime
before they merge in the LIGO/Virgo band. For a proof-of-concept, we show that
the eccentricity oscillations of these binaries can be detected with LISA for
BHBs in the local universe up to a few Mpcs, with observation periods shorter
than the mission lifetime, thereby disentangling this merger channel from
others. The approach presented here is straightforward to apply to a wide
variety of compact object binaries with a tertiary companion.
