A measurement of the parity-violating decay asymmetry parameter, ab, and the helicity amplitudes for the decay.Lambda(0)(b) -> J/psi(mu(+) mu(-)) Lambda(0)(p pi(-)) is reported. The analysis is based on 1400 Lambda(0)(b)and (Lambda) over bar (0)(b) baryons selected in 4.6 fb(-1) of proton-proton collision data with a center-of-mass energy of 7 TeV recorded by the ATLAS experiment at the LHC. By combining the.0 b and. _ 0 b samples under the assumption of CP conservation, the value of ab is measured to be 0.30 +/- 0.16(stat) +/- 0.06(syst). This measurement provides a test of theoretical models based on perturbative QCD or heavy-quark effective theory.