A complete study of teh angualr distributions of the process Lambda_b to Lambda V(1-) with lambda to p pi- and V(J/Psi) to l+l- or V(rho0,omega, phi) to pi+ pi-, K+K- is performed. Emphasis is put on the initial Lambda-b polarization produced in the proton-proton collisions and, without any dynamical assumption, polarized density-matrices of the vector-mesons V are derived and help to construct T-odd observables which allow us to perform tests of both Time-Reversal and CP violation