Exclusive semileptonic Lambda_b decays to excited charmed Lambda_c baryons are investigated at order Lambda_QCD/m_Q in the heavy quark effective theory. The differential decay rates are analyzed for the J^π=1/2^- Lambda_c(2593) and the J^π=3/2^- Λ_c(2625). They receive 1/m_c,b corrections at zero recoil that are determined by mass splittings and the leading order Isgur-Wise function. With some assumptions, we find that the branching fraction for Lambda_b decays to these states is 2.5-3.3 3/2

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... tes, which vanishes for m_Q →∞, remains small at order Lambda_QCD/m_Q since 1/m_c corrections do not contribute. Matrix elements of weak currents between a Lambda_b and other excited Lambda_c states are analyzed at zero-recoil to order Lambda_QCD/m_Q. Applications to baryonic heavy quark sum-rules are explored.