  Electromagnetic (EM) counterparts to supermassive black hole binary mergers
observed by LISA can be localized to within the field of view of astronomical
instruments ~10 deg^2 hours to weeks prior to coalescence. The temporal
coincidence of any prompt EM counterpart with a gravitationally-timed merger
may offer the best chance of identifying a unique host galaxy. We discuss the
challenges posed by searches for prompt EM counterparts and propose novel
observational strategies to address them. In particular, we discuss the size
and shape evolution of the LISA localization error ellipses on the sky, and
quantify the requirements for dedicated EM surveys of the area prior to
coalescence. A triggered EM counterpart search campaign will require monitoring
a several-square degree area. It could aim for variability at the 24-27 mag
level in optical bands, for example, which corresponds to 1-10% of the
Eddington luminosity of the prime LISA sources of 10^6-10^7 Msun BHs at z=1-2,
on time-scales of minutes to hours, the orbital time-scale of the binary in the
last 2-4 weeks. A cross-correlation of the period of any variable EM signal
with the quasi-periodic gravitational waveform over 10-1000 cycles may aid the
detection. Alternatively, EM searches can detect a transient signal
accompanying the coalescence. We highlight the measurement of differences in
the arrival times of photons and gravitons from the same cosmological source as
a valuable independent test of the massive character of gravity, and of
possible violations of Lorentz invariance in the gravity sector.
