  A complete study of the angular distributions of the processes, $\Lambda_b
\to {\Lambda} V(1^-)$, with $\Lambda \to p {\pi}^-$ and $V (J/{\Psi}) \to
{\ell}^+ {\ell}^-$ or $V ({\rho}^0,\omega) \to {\pi}^+ {\pi}^-,$ is performed.
  Emphasis is put on the initial $\Lambda_b$ polarization produced in the
proton-proton collisions. The polarization density-matrices as well as angular
distributions are derived and help to construct T-odd observables which allow
us to perform tests of both Time-Reversal and CP violation.
