Spin induced precessional modulations of gravitational wave signals from supermassive black hole binaries can improve the estimation of luminosity distance to the source by space based gravitational wave missions like the Laser Interferometer Space Antenna (LISA). We study how this impacts the ability of LISA to do cosmology, specifically, to measure the dark energy equation of state (EOS) parameter w. Using the ΛCDM model of cosmology, we show that observations of precessing binaries with mass ratio 10∶1 by LISA, combined with a redshift measurement, can improve the determination of w up to an order of magnitude with respect to the nonprecessing case depending on the total mass and the redshift.