We present a search for the decays of B-0 mesons into a final state containing a Lambda baryon and missing energy. These results are obtained from a 711 fb(-1) data sample that contains 772 x 10(6) B (B) over bar pairs and was collected near the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We use events in which one B meson is fully reconstructed in a hadronic decay mode and require the remainder of the event to consist of only a single A. No evidence for these decays is found, and we set 90% confidence level upper limits on the branching fractions in the range 2.1-3.8 x 10(-5). This measurement provides the world's most restrictive limits, with implications for baryogenesis and dark matter production.