Ori and Thorne have discussed the duration and observability (with LISA) of the transition from circular, equatorial inspiral to plunge for stellar-mass objects into supermassive (10(5)-10(8)M) Kerr black holes. We extend their computation to eccentric Kerr equatorial orbits. Even with orbital parameters near exactly determined, we find that there is no universal length for the transition; rather, the length of the transition depends sensitively-essentially randomly-on initial conditions. Still, the Ori-Thorne zero-eccentricity results are essentially an upper bound on the length of eccentric transitions involving similar bodies (e.g., a fixed). Hence the implications for observations are no better: if the massive body is M=10(6)M, the captured body has a mass m, and the process occurs at distance d from LISA, then S/Nless than or similar to(m/10M)(1Gpc/d)xO(1), with the precise constant depending on the black hole spin. For low-mass bodies (mless than or similar to7M) for which the event rate is at least vaguely understood, we expect little chance (probably [much] less than 10%, depending strongly on the astrophysical assumptions) of LISA detecting a transition event with S/N>5 during its run; however, even a small infusion of higher-mass bodies or a slight improvement in LISA's noise curve could potentially produce S/N>5 transition events during LISA's lifetime.
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