  We evaluate the cosmological coalescence and detection rates for massive
black hole (MBH) binaries targeted by the gravitational wave observatory Laser
Interferometer Space Antenna (LISA). Our calculation starts with a population
of gravitationally unbound MBH pairs, drawn from the TNG50-3 cosmological
simulation, and follows their orbital evolution from kpc scales all the way to
coalescence using a semi-analytic model developed in our previous work. We find
that for a majority of MBH pairs that coalesce within a Hubble time dynamical
friction is the most important mechanism that determines their coalescence
rate. Our model predicts a MBH coalescence rate < 0.45/ yr and a LISA detection
rate < 0.34/ yr. Most LISA detections should originate from 10^6 - 10^6.8 solar
masses MBHs in gas-rich galaxies at redshifts 1.6 < z < 2.4, and have a
characteristic signal to noise ratio SNR ~ 100. We however find a dramatic
reduction in the coalescence and detection rates, as well as the average SNR,
if the effects of radiative feedback from accreting MBHs are taken into
account. In this case, the MBH coalescence rate is reduced by 78% (to < 0.1/
yr), and the LISA detection rate is reduced by 94% (to 0.02/ yr), whereas the
average SNR is ~ 10. We emphasize that our model provides a lower limit on the
LISA detection rate, consistent with other works in the literature that draw
their MBH pairs from cosmological simulations.
