We have searched for tau lepton decays, tau(-) -> Lambda($) over bar pi(-) and tau -> Lambda pi(-), that simultaneously violate the conservation of the lepton (L) and baryon (B) number using a data sample of 154 fb(-1) collected with the Belle detector at the KEKB e(+)e(-) asymmetric-energy collider. No evidence for a signal was found in either of the decay modes and we set the following upper limits for the branching fractions: B(tau(-) -> Lambda($) over bar pi(-)) < 1.4 x 10(-7) and B(tau(-) -> Lambda($) over bar pi(-)) < 0.72 x 10(-7) at the 90% confidence level. This is the first search ever performed for these modes. (c) 2005 Elsevier B.V. All rights reserved.