Using about 1.5 million hadronic Z decays recorded with the ALEPH dete
ctor, the lifetime of the b baryons has been measured using two indepe
ndent data samples. From a maximum likelihood fit to the impact parame
ter distribution of leptons in 519 Lambda l(-) combinations containing
a b baryon sample of 290 decays, the measured b baryon lifetime is ta
u(b-baryon) = 1.05(-0.11)(+0.12)(stat) +/-0.09(syst) ps. The lifetime
of the Lambda(b)(0) baryon from a maximum likelihood fit to the proper
time distribution of 58 Lambda(c)(+)l(-) candidates containing a Lamb
da(b)(0) sample of 44 decays, is tau(Lambda b0) = 1.02(-0.18)(+0.23)(s
tat) +/- 0.06(syst) ps.