The Lambda b differential production cross section and the cross section ratio sigma((Lambda) over bar (b))/sigma(Lambda(b)) are measured as functions of transverse momentum p(T)(Lambda b) rapidity vertical bar y(Lambda b)vertical bar in pp collisions at root s = 7 TeV using data collected by the CMS experiment at the LHC. The measurements are based on Lambda(b) decays reconstructed in the exclusive final state J/psi Lambda, with the subsequent decays J/psi -> mu(+)mu(-) and Lambda -> p pi, using a data sample corresponding to an integrated luminosity of 1.9 fb(-1). The product sigma(Lambda(b)) x B(Lambda(b) -> J/psi Lambda) versus p(T)(Lambda b) falls faster than that of b mesons. The measured value of sigma(Lambda(b)) x B(Lambda(b) -> J/psi Lambda) for p(T)(Lambda b) > 10 GeV and vertical bar y(Lambda b)vertical bar < 2.0 is 1.16 +/- 0.06 +/- 0.12 nb, and the integrated sigma(<(Lambda)over bar>(b))/sigma(Lambda(b)) ratio is 1.02 +/- 0.07 +/- 0.09, where the uncertainties are statistical and systematic, respectively. (C) 2012 CERN. Published by Elsevier B.V. All rights reserved.