  The Laser Interferometer Space Antenna (LISA) guarantees the detection of
gravitational waves by monitoring a handful of known nearby galactic binary
systems, the so-called ``verification binaries''. We consider the most updated
information on the source parameters for the thirty more promising verification
binaries. We investigate which of them are indeed guaranteed sources for LISA
and estimate the accuracy of the additional information that can be extracted
during the mission. Our analysis considers the two independent Michelson
outputs that can be synthesised from the LISA constellation, and we model the
LISA transfer function using the rigid adiabatic approximation. We carry out
extensive Monte Carlo simulations to explore the dependency of our results on
unknown or poorly constrained source parameters. We find that four sources --
RXJ0806.3+1527, V407 Vul, ES Cet and AM CVn -- are clearly detectable in one
year of observation; RXJ0806.3+1527 should actually be observable in less than
a week. For these sources LISA will also provide information on yet unknown
parameters with an error between approximately 1 percent and 10 percent. Four
additional binary systems -- HP Lib, 4U 1820-30, WZ Sge and KPD 1930+2752 --
might also be marginally detectable.
