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Electromagnetic (EM) counterparts to supermassive black hole binary mergersobserved by LISA can be localized to within the field of view of astronomicalinstruments ~10 deg^2 hours to weeks prior to coalescence. The temporalcoincidence of any prompt EM counterpart with a gravitationally-timed mergermay offer the best chance of identifying a unique host galaxy. We discuss thechallenges posed by searches for prompt EM counterparts and propose novelobservational strategies to address them. In particular, we discuss the sizeand shape evolution of the LISA localization error ellipses on the sky, andquantify the requirements for dedicated EM surveys of the area prior tocoalescence. A triggered EM counterpart search campaign will require monitoringa several-square degree area. It could aim for variability at the 24-27 maglevel in optical bands, for example, which corresponds to 1-10% of theEddington 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 thelast 2-4 weeks. A cross-correlation of the period of any variable EM signalwith the quasi-periodic gravitational waveform over 10-1000 cycles may aid thedetection. Alternatively, EM searches can detect a transient signalaccompanying the coalescence. We highlight the measurement of differences inthe arrival times of photons and gravitons from the same cosmological source asa valuable independent test of the massive character of gravity, and ofpossible violations of Lorentz invariance in the gravity sector.

Pre-Merger Localization of Gravitational-Wave Standard Sirens With LISA: Triggered Search for an Electromagnetic Counterpart