  ESA and NASA are moving forward with plans to launch LISA around 2034. With
data from the Illustris cosmological simulation, we provide analysis of LISA
detection rates accompanied by characterization of the merging massive black
hole population. Massive black holes of total mass $\sim10^5-10^{10} M_\odot$
are the focus of this study. We evolve Illustris massive black hole mergers,
which form at separations on the order of the simulation resolution ($\sim$kpc
scales), through coalescence with two different treatments for the binary
massive black hole evolutionary process. The coalescence times of the
population, as well as physical properties of the black holes, form a
statistical basis for each evolutionary treatment. From these bases, we Monte
Carlo synthesize many realizations of the merging massive black hole population
to build mock LISA detection catalogs. We analyze how our massive black hole
binary evolutionary models affect detection rates and the associated parameter
distributions measured by LISA. With our models, we find massive black hole
binary detection rates with LISA of $\sim0.5-1$ yr$^{-1}$ for massive black
holes with masses greater than $10^5M_\odot$. This should be treated as a lower
limit primarily because our massive black hole sample does not include masses
below $10^5M_\odot$, which may significantly add to the observed rate. We
suggest reasons why we predict lower detection rates compared to much of the
literature.
