The kinematic dependences of the relative production rates, f(Lambda b)(0)/f(d), of Lambda(0)(b) baryons and B-0 mesons are measured using Lambda(0)(b) -> Lambda(+)(c)pi(-) and (B) over bar (0) -> D+pi(-) decays. The measurements use proton-proton collision data, corresponding to an integrated luminosity of 1 fb(-1) at a centre-of-mass energy of 7 TeV, recorded in the forward region with the LHCb experiment. The relative production rates are observed to depend on the transverse momentum, pT, and pseudorapidity, eta, of the beauty hadron, in the studied kinematic region 1.5 < pT < 40 GeV/c and 2 < eta < 5. Using a previous LHCb measurement of f(Lambda b)(0)/f(d) in semileptonic decays, the branching fraction B (Lambda(0)(b) -> Lambda(+)(c)pi(-)) = (4.30 +/- 0.03(-0.11)(+0.12)+/- 0.26 +/- 0.21) x 10(-3) is obtained, where the first uncertainty is statistical, the second is systematic, the third is from the previous LHCb measurement of f(Lambda b)(0)/f(d) and the fourth is due to the (B) over bar (0) -> D+pi(-) branching fraction. This is the most precise measurement of a Lambda(0)(b) branching fraction to date.