  Despite their potential role as massive seeds for quasars, in dwarf galaxy
feedback, and in tidal disruption events, the observational evidence for
intermediate-mass black holes (IMBHs) is scarce. LISA may observe stellar-mass
black hole binaries orbiting Galactic IMBHs, and reveal the presence of the
IMBH by measuring the Doppler shift in the gravitational waveform induced by
the binary's radial velocity. We estimate the number of detectable Doppler
shift events from the Milky Way globular clusters (assuming they host IMBHs)
and we find that it decreases with the IMBH mass. A few Galactic globular
clusters (including M22 and $\omega$ Centauri) may produce at least one event
detectable by LISA. Even in more pessimistic scenarios, one could still expect
$\sim$ 1 event overall in the Milky Way. We also estimate the number of Doppler
shift events for IMBHs wandering in the Milky Way as a result of the disruption
of their parent clusters. If there is at least one binary black hole orbiting
around each wandering IMBH, LISA may detect up to a few tens of Doppler shift
events from this elusive IMBH population. Under more pessimistic assumptions,
LISA may still detect $\sim 1$ wandering IMBH that would hardly be observable
otherwise.
