Improvements will have been made by high-redshift observations of quasi-stellar objects (QSOs) and protogalaxies from missions like the JWST, EUCLID and the Wide-Field Infrared Survey Telescope (WFIRST), and by the Atacama Large Millimeter/submillimeter Array (ALMA) on the ground.
These observations may well have constrained the supermassive black hole mass spectrum from a few times 1010 solar masses, or even higher, down to around 107 solar masses, but probably not into the main LISA range of 104 – 106 solar masses.
LISA observations will fill this gap and also provide a check on selection effects and other systematics of the electromagnetic observations. By measuring the mass and spins of massive black holes as a function of redshift out to z = 20 or so, LISA will greatly improve models of how ultra-massive black holes grow so quickly, and what roles accretion and mergers play in the growth of all massive black holes. LISA observations of mergers of 104 – 105 solar mass Black holes out to z = 20 can provide a strict test of the amount of growth by merger expected in these models.