SMBH [@chen19].

The difficulty would be alleviated if the BBH can be detected by a space-borne GW observatory, such as the Laser Interferometer Space Antenna [LISA, @danzmann_2017]. LISA is sensitive to milli-Hertz (mHz) GWs and hence can capture a BBH at the early inspiral phase, weeks to millennia before it enters the LIGO/Virgo band [@miller02; @sesana16; @moore19]. Using the chirp signal, LISA can also measure the (redshifted) mass of the BBH. In this way, LISA may detect hundreds of massive BBHs during its mission duration of $4-5$ years [@sesana16; @kyutoku16; @lamberts18; @kremer18] and compare their masses with those from LIGO/Virgo observations.

Moreover, by tracking the BBHs with a decent signal-to-noise ratio (SNR, e.g., $>10$ ) for several months to years, LISA may reveal multiple images of a GW source if it is strongly lensed [@seto04; @sereno11]. The long signal may also reveal a shift of the GW phase caused by the wave effect of gravitational lensing [@nakamura98; @takahashi03lensing]. Moreover, if a BBH is close to a SMBH, the long waveform should also contain imprints of the orbital motion of the binary around the SMBH [@inayoshi17; @meiron17; @robson18; @chamberlain19; @tamanini19; @wong19; @torres-orjuela20] or the perturbation of the binary orbit by the 