  The Laser Interferometer Space Antenna (LISA) gravitational-wave (GW)
observatory will be limited in its ability to detect mergers of binary black
holes (BBHs) in the stellar-mass range. A future ground-based detector network,
meanwhile, will achieve by the LISA launch date a sensitivity that ensures
complete detection of all mergers within a volume $>\!\mathcal{O}(10)\,{\rm
Gpc}^{3}$. We propose a method to use the information from the ground to
revisit the LISA data in search for sub-threshold events. By discarding
spurious triggers that do not overlap with the ground-based catalogue, we show
that the signal-to-noise threshold $\rho_{\rm LISA}$ employed in LISA can be
significantly lowered, greatly boosting the detection rate. The efficiency of
this method depends predominantly on the rate of false-alarm increase when the
threshold is lowered and on the uncertainty in the parameter estimation for the
LISA events. As an example, we demonstrate that while all current LIGO
BBH-merger detections would have evaded detection by LISA when employing a
standard $\rho_{\rm LISA}=8$ threshold, this method will allow us to easily
(possibly) detect an event similar to GW150914 (GW170814) in LISA. Overall, we
estimate that the total rate of stellar-mass BBH mergers detected by LISA can
be boosted by a factor $\sim\!4$ ($\gtrsim\!8$) under conservative (optimistic)
assumptions. This will enable new tests using multi-band GW observations,
significantly aided by the greatly increased lever arm in frequency.
