We report the detection of the Pb i lambda4057.8 line in the very metal-poor (&sqbl0;Fe&solm0;H&sqbr0;=-2.7), carbon-rich star, LP 625-44. We determine the abundance of Pb (&sqbl0;Pb&solm0;Fe&sqbr0;=2.65) and 15 other neutron-capture elements. The abundance pattern between Ba and Pb agrees well with a scaled solar system s-process component, while the lighter elements (Sr-Zr) are less abundant than Ba. The enhancement of s-process elements is interpreted as a result of mass transfer in a binary system from a previous asymptotic giant branch (AGB) companion, an interpretation strongly supported by radial velocity variations of this system. The detection of Pb makes it possible, for the first time, to compare model predictions of s-process nucleosynthesis in AGB stars with observations of elements between Sr and Pb. The Pb abundance is significantly lower than the prediction of recent models (e.g., Gallino et al.), which succeeded in explaining the metallicity dependence of the abundance ratios of light s-elements (Sr-Zr) to heavy ones (Ba-Dy) found in previously observed s-process-enhanced stars. This suggests that one should either (1) reconsider the underlying assumptions concerning the (13)C-rich s-processing site ((13)C pocket) in the present models or (2) investigate alternative sites of s-process nucleosynthesis in very metal-poor AGB stars.