Possible manifestation of the family non-universal Z' boson effects in lepton polarization in rare, exclusive baryonic Lambda(b) -> Lambda l(+)l(-) decay is examined. It is observed that the double lepton polarizations P-NN. P-TT and P-TN are sensitive to the Z' contribution. Moreover, it is found that the values of the polarized forward-backward asymmetry A(FB)(LL) are different in Standard Model (SM) and family non-universal Z' model in different regions of q(2), and therefore can serve as an efficient tool for establishing new physics beyond the SM. (C) 2012 Elsevier B.V. All rights reserved.