We report a measurement of the Lambda(b)(0) lifetime using a sample corresponding to 1.3 fb(-1) of data collected by the D0 experiment in 2002-2006 during run II of the Fermilab Tevatron collider. The Lambda(b)(0) baryon is reconstructed via the decay Lambda(b)(0)-->micronuLambda(c)(+)X. Using 4437+/-329 signal candidates, we measure the Lambda(b)(0) lifetime to be tau(Lambda(b)(0))=1.290(-0.110)(+0.119)(stat)(-0.091)(+0.087)(syst) ps, which is among the most precise measurements in semileptonic Lambda(b)(0) decays. This result is in good agreement with the world average value.