  We present measurements of the Lambda^0_b lifetime in the exclusive decay
channel Lambda^0_{b}->J/psi Lambda^0, with J/psi to mu+ mu- and Lambda^0 to p
pi-, the B^0 lifetime in the decay B^0 -> J/psi K^0_S with J/psi to mu+ mu- and
K^0_S to pi+ pi-, and the ratio of these lifetimes. The analysis is based on
approximately 250 pb^{-1} of data recorded with the D0 detector in pp(bar)
collisions at sqrt{s}=1.96 TeV. The Lambda^0_b lifetime is determined to be
tau(Lambda^0_b) = 1.22 +0.22/-0.18 (stat) +/- 0.04 (syst) ps, the B^0 lifetime
tau(B^0) = 1.40 +0.11/-0.10 (stat) +/- 0.03 (syst) ps, and the ratio
tau(Lambda^0_b)/tau(B^0) = 0.87 +0.17/-0.14 (stat) +/- 0.03 (syst). In contrast
with previous measurements using semileptonic decays, this is the first
determination of the Lambda^0_b lifetime based on a fully reconstructed decay
channel.
