We study the decays of   $ \Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^- $   with   $ \Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^- $  . We examine the full angular distributions with polarized   $ \Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^- $  , where the T-odd observables are identified. We discuss the possible effects of new physics (NP) and find that the T-odd observables are sensitive to them as they vanish in the standard model. Special attention is given to the interference of (pseudo)scalar operators with (axial)vector operators in polarized   $ \Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^- $  , which are studied for the first time. Their effects are proportional to the lepton masses and therefore may evade the constraint from   $ \Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^- $   at the LHCb naturally. As   $ \Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^- $   is uncontaminated by the charmonia resonance, it provides a clean background to probe NP. In addition, we show that the experimental central value of   $ \Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^- $   in   $ \Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^- $   at the LHCb can be explained by the NP case, which couples to the right-handed quarks and leptons. The polarization fraction of   $ \Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^- $   at the LHCb is found to be consistent with zero regardless of the NP scenarios.