  We examine expected effective spin ($\chi_{{\rm eff},1\rm yr}$) and orbital
eccentricity ($e_{1\rm yr}$) correlations for a population of observable
equal-mass massive black hole binaries (MBHBs) with total redshifted mass
$M_z\sim[10^{4.5},10^{7.5}]~{\rm M}_\odot$ embedded in a circumbinary disc
(CBD), one-year before merging in the LISA band. We find a strong correlation
between measurable eccentricity and negative effective spin for MBHBs that are
carried to merger by retrograde accretion. This is due to the well-established
eccentricity pumping of retrograde accretion and the formation of retrograde
CBD-aligned mini-discs, as observed in hydrodynamical simulations. Conversely,
prograde accretion channels result in positive $\chi_{{\rm eff},1\rm yr}$ and
non-measurable $e_{1\rm yr}$. This clear contrast between the two CBD
orientations -- and particularly the unique signature of retrograde
configurations -- provides a promising way to unlock the mysteries of MBHB
formation channels in the LISA era.
