We carry out an analysis of the multibody decay cascade Λ b → Λ * J J/ψ → pK − J/ψ with the Λ * J resonance including Λ * 1520 , Λ * 1600 , and Λ * 1800 , and J/ψ reconstructed by the lepton pair final state. Using the helicity amplitude technique, we derive a compact form for the angular distributions for the decay chain, from which one can extract various one-dimensional distributions. Using the Λ b → Λ * J form factors from Lattice QCD and quark model, we calculate the differential and integrated partial widths. Decay branching fractions are found as B(Λ b → pKµ + µ − ) = (1.41 ± 0.31) × 10 −5 , B(Λ b → pKe + e − ) = (1.41±0.32)×10 −5 . In addition, we also explore forward-backward asymmetry, and various polarizations. Results in this work will serve a calibration for the study of b → sμµ decays in Λ b decays in future and provide useful information towards the understanding of the properties of the Λ * J baryons.