  Observations of binary inspirals with LISA will allow us to place bounds on
alternative theories of gravity and to study the merger history of massive
black holes (MBH). These possibilities rely on LISA's parameter estimation
accuracy. We update previous studies of parameter estimation including
non-precessional spin effects. We work both in Einstein's theory and in
alternative theories of gravity of the scalar-tensor and massive-graviton
types. Inclusion of non-precessional spin terms in MBH binaries has little
effect on the angular resolution or on distance determination accuracy, but it
degrades the estimation of the chirp mass and reduced mass by between one and
two orders of magnitude. The bound on the coupling parameter of scalar-tensor
gravity is significantly reduced by the presence of spin couplings, while the
reduction in the graviton-mass bound is milder. LISA will measure the
luminosity distance of MBHs to better than ~10% out to z~4 for a (10^6+10^6)
Msun binary, and out to z~2 for a (10^7+10^7) Msun binary. The chirp mass of a
MBH binary can always be determined with excellent accuracy. Ignoring spin
effects, the reduced mass can be measured within ~1% out to z=10 and beyond for
a (10^6+10^6) Msun binary, but only out to z~2 for a (10^7+10^7) Msun binary.
Present-day MBH coalescence rate calculations indicate that most detectable
events should originate at z~2-6: at these redshifts LISA can be used to
measure the two black hole masses and their luminosity distance with sufficient
accuracy to probe the merger history of MBHs. If the low-frequency LISA noise
can only be trusted down to 10^-4 Hz, parameter estimation for MBHs (and LISA's
ability to perform reliable cosmological observations) will be significantly
degraded.
