  The Laser Interferometer Space Antenna (LISA) will observe black hole
binaries of stellar origin during their gravitational wave inspiral, months to
years before coalescence. Due to the long duration of the signal in the LISA
band, a faithful waveform is necessary in order to keep track of the binary
phase. This is crucial to extract the signal from the data and to perform an
unbiased estimation of the source parameters. We consider Post-Newtonian (PN)
waveforms, and analyze the PN order needed to keep the bias caused by the PN
approximation negligible relative to the statistical parameter estimation
error, as a function of the source parameters. By considering realistic
population models, we conclude that for $\sim 90\%$ of the stellar black hole
binaries detectable by LISA, waveforms at low Post-Newtonian (PN) order (PN
$\le 2$) are sufficiently accurate for an unbiased recovery of the source
parameters. Our results provide a first estimate of the trade-off between
waveform accuracy and information recovery for this class of LISA sources.
