  The continuous improvement in localization errors (sky position and distance)
in real time as LISA observes the gradual inspiral of a supermassive black hole
(SMBH) binary can be of great help in identifying any prompt electromagnetic
counterpart associated with the merger. We develop a new method, based on a
Fourier decomposition of the time-dependent, LISA-modulated gravitational-wave
signal, to study this intricate problem. The method is faster than standard
Monte Carlo simulations by orders of magnitude. By surveying the parameter
space of potential LISA sources, we find that counterparts to SMBH binary
mergers with total mass M~10^5-10^7 M_Sun and redshifts z<~3 can be localized
to within the field of view of astronomical instruments (~deg^2) typically
hours to weeks prior to coalescence. This will allow targeted searches for
variable electromagnetic counterparts as the merger proceeds, as well as
monitoring of the most energetic coalescence phase. A rich set of astrophysical
and cosmological applications would emerge from the identification of
electromagnetic counterparts to these gravitational-wave standard sirens.
