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A binary compact object early in its inspiral phase will be picked up by itsnearly monochromatic gravitational radiation by LISA. But even this innocuousappearing candidate poses interesting detection challenges. The data that willbe scanned for such sources will be a set of three functions of LISA's twelvedata streams obtained through time-delay interferometry, which is necessary tocancel the noise contributions from laser-frequency fluctuations andoptical-bench motions to these data streams. We call these three functionspseudo-detectors. The sensitivity of any pseudo-detector to a given skyposition is a function of LISA's orbital position. Moreover, at a given pointin LISA's orbit, each pseudo-detector has a different sensitivity to the samesky position. In this work, we obtain the optimal statistic for detectinggravitational wave signals, such as from compact binaries early in theirinspiral stage, in LISA data. We also present how the sensitivity of LISA,defined by this optimal statistic, varies as a function of sky position andLISA's orbital location. Finally, we show how a real-time search for inspiralsignals can be implemented on the LISA data by constructing a bank of templatesin the sky positions.Comment: 22 pages, 15 eps figures, Latex, uses iopart style/class files. Based  on talk given at the 8th Gravitational Wave Data Analysis Workshop,  Milwaukee, USA, December 17-20, 2003. Accepted for publication in Class.  Quant. Gra

Optimal statistic for detecting gravitational wave signals from binary inspirals with LISA