  We calculate the gravitational wave signal from the growth of 10 million
solar mass supermassive black holes (SMBH) from the remnants of Population III
stars. The assembly of these lower mass black holes is particularly important
because observing SMBHs in this mass range is one of the primary science goals
for the Laser Interferometer Space Antenna (LISA), a planned NASA/ESA mission
to detect gravitational waves. We use high resolution cosmological N-body
simulations to track the merger history of the host dark matter halos, and
model the growth of the SMBHs with a semi-analytic approach that combines
dynamical friction, gas accretion, and feedback. We find that the most common
source in the LISA band from our volume consists of mergers between
intermediate mass black holes and SMBHs at redshifts less than 2.
  This type of high mass ratio merger has not been widely considered in the
gravitational wave community; detection and characterization of this signal
will likely require a different technique than is used for SMBH mergers or
extreme mass ratio inspirals. We find that the event rate of this new LISA
source depends on prescriptions for gas accretion onto the black hole as well
as an accurate model of the dynamics on a galaxy scale; our best estimate
yields about 40 sources with a signal-to-noise ratio greater than 30 occur
within a volume like the Local Group during SMBH assembly -- extrapolated over
the volume of the universe yields roughly 500 observed events over 10 years,
although the accuracy of this rate is affected by cosmic variance.
