  The Laser Interferometer Space Antenna (LISA) is expected to detect close
white dwarf binaries (CWDBs) through their gravitational radiation. Around 3000
binaries will be spectrally resolved at frequencies > 3 mHz, and their
positions on the sky will be determined to an accuracy ranging from a few tens
of arcminutes to a degree or more. Due to the small binary separation, the
optical light curves of >~ 30% of these CWDBs are expected to show eclipses,
giving a unique signature for identification in follow-up studies of the LISA
error boxes. While the precise optical location improves binary parameter
determination with LISA data, the optical light curve captures additional
physics of the binary, including the individual sizes of the stars in terms of
the orbital separation. To optically identify a substantial fraction of CWDBs
and thus localize them very accurately, a rapid monitoring campaign is
required, capable of imaging a square degree or more in a reasonable time, at
intervals of 10--100 seconds, to magnitudes between 20 and 25. While the
detectable fraction can be up to many tens of percent of the total resolved
LISA CWDBs, the exact fraction is uncertain due to unknowns related to the
white dwarf spatial distribution, and potentially interesting physics, such as
induced tidal heating of the WDs due to their small orbital separation.
