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We present measurements of the Λb0 lifetime in the exclusive decay channel Λb0 → J/ψΛ0, with J/ψ → μ+μ- and Λ0 → pπ-, the B0 lifetime in the decay Λ0 → J/ψKs0 with J/ψ → μ+μ- and Ks0 → π+π-, and the ratio of these lifetimes. The analysis is based on approximately 250 pb-1 of data recorded with the D0 detector in pp̅ collisions at √s = 1.96 TeV. The Λb0 lifetime is determined to be τ(Λb0) = 1.22-0.18+0.22(stat) ± 0.04(syst) ps, the B0 lifetime τ(B0) = 1.40-0.10+0.11(stat) ± 0.03(syst) ps, and the ratio τ(Λb0)/τ(B0) = 0.87-0.14+0.17 (stat) ± 0.03(syst). In contrast with previous measurements using semileptonic decays, this is the first determination of the Λb0 lifetime based on a fully reconstructed decay channel.