Putting together kinematical and dynamical analysis, a complete study of the decay channels Lambda_b to Lambda V(-1) with Lambda to p pi- and V(J/Psy) to l+ l- or V(rho0) to pi+ pi- is presented. An intensive use of the helicity formalism is involved on the kinematical side, while on the dynamical side, HQET is applied to determine the hadronic matrix elements between the baryons Lambda_b and Lambda. CP and time reversal symmetries are investigated in these channels where the major role of the Lambda_b polarization for constructing T-odd observables is emphasized.