We search for the rare flavor-changing neutral current process $B^- to Lambda {overline p} u{overline{ u}}$ using data from the BABAR experiment. A total of 424 fb$^{-1}$ of $e^+e^-$ collision data collected at the center-of-mass energy of the $Upsilon$(4S) resonance is used in this study, corresponding to a sample of ${(471 pm 3) times 10^{6}}$ $Boverline{B}$ pairs. Signal $B^- to Lambda {overline p} u{overline{ u}}$ candidates are identified by first fully reconstructing a $B^+$ decay in one of many possible exclusive decays to hadronic final states, then examining detector activity that is not associated with this reconstructed $B^+$ decay for evidence of a signal $B^- to Lambda {overline p} u{overline{ u}}$ decay. The data yield is found to be consistent with the expected background contribution under a null signal hypothesis, resulting in an upper limit of ${{cal B} (B^- to Lambda {overline p} u{overline{ u}}) < 3.0times 10^{-5}}$ at the $90%$ confidence level.