  Inspirals of stellar-mass compact objects into $\sim 10^6 M_{\odot}$ black
holes are especially interesting sources of gravitational waves for LISA. We
investigate whether the emitted waveforms can be used to strongly constrain the
geometry of the central massive object, and in essence check that it
corresponds to a Kerr black hole (BH). For a Kerr BH, all multipole moments of
the spacetime have a simple, unique relation to $M$ and $S$, the BH's mass and
spin; in particular, the spacetime's mass quadrupole moment is given by $Q=-
S^2/M$. Here we treat $Q$ as an additional parameter, independent of $M$ and
$S$, and ask how well observation can constrain its difference from the Kerr
value. This was already estimated by Ryan, but for simplified (circular,
equatorial) orbits, and neglecting signal modulations due to the motion of the
LISA satellites. Here we consider generic orbits and include these modulations.
We use a family of approximate (post-Newtonian) waveforms, which represent the
full parameter space of Inspiral sources, and exhibit the main qualitative
features of true, general relativistic waveforms. We extend this parameter
space to include (in an approximate manner) an arbitrary value of $Q$, and
construct the Fisher information matrix for the extended parameter space. By
inverting the Fisher matrix we estimate how accurately $Q$ could be extracted
from LISA observations. For 1 year of coherent data from the inspiral of a $10
M_{\odot}$ BH into rotating BHs of masses $10^{5.5} M_{\odot}$, $10^6
M_{\odot}$, or $10^{6.5} M_{\odot}$, we find $\Delta (Q/M^3) \sim 10^{-4}$,
$10^{-3}$, or $10^{-2}$, respectively (assuming total signal-to-noise ratio of
100, typical of the brightest detectable EMRIs). These results depend only
weakly on the eccentricity of the orbit or the BH's spin.
