  We study the decays of $\Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^-$
with $\ell = (e, \mu, \tau)$. In particular, we examine the full angular
distributions with polarized $\Lambda_b$ and identify the time-reversal
asymmetries or T-odd observables. By using the homogeneous bag model, we find
that the decay branching fractions of $\Lambda_b \to \Lambda \ell^+\ell^-$ are
$(9.1\pm 2.5,7.9\pm 1.8, 2.1\pm 0.2)\times 10^{-7}$ for $\ell =(e, \mu ,\tau)$,
respectively. In addition, we obtain that $A_{FB}^{\ell} = -0.369\pm 0.007$ and
$A_{FB}^{h}=-0.333\pm 0.004$, averaged in the range of $15 \leq q^2 \leq 20~
\text{GeV}^2$. These results are well consistent with the current experimental
data. We also explore the T-odd observables in $\Lambda_b \to \Lambda(\to p
\pi^-) \mu^+ \mu^-$, which are sensitive to new physics~(NP). Explicitly, we
illustrate that the current experimental measurement from one of the T-odd
observables favors the existence of NP, such as the extra $Z$-boson model.
