  LISA can detect higher harmonics of the ringdown gravitational-wave signal
from massive black-hole binary mergers with large signal-to-noise ratio. The
most massive black-hole binaries are more likely to have electromagnetic
counterparts, and the inspiral will contribute little to their signal-to-noise
ratio. Here we address the following question: can we extract the binary
parameters and localize the source using LISA observations of the ringdown
only? Modulations of the amplitude and phase due to LISA's motion around the
Sun can be used to disentangle the source location and orientation when we
detect the long-lived inspiral signal, but they can not be used for
ringdown-dominated signals, which are very short-lived. We show that (i) we can
still measure the mass ratio and inclination of high-mass binaries by carefully
combining multiple ringdown harmonics, and (ii) we can constrain the sky
location and luminosity distance by relying on the relative amplitudes and
phases of various harmonics, as measured in different LISA channels.
