  We comparatively analyze the rare $\Lambda _b\rightarrow \Lambda \ell^+
\ell^-$ channel in standard model, supersymmetry and Randall-Sundrum model with
custodial protection (RS$_c$). Using the parametrization of the matrix elements
entering the low energy effective Hamiltonian in terms of form factors, we
calculate the corresponding differential decay width and lepton
forward-backward asymmetry in these models. We compare the results obtained
with the most recent data from LHCb as well as lattice QCD results on the
considered quantities. It is obtained that the standard model, with the form
factors calculated in light-cone QCD sum rules, can not reproduce some
experimental data on the physical quantities under consideration but the
supersymmetry can do it. The RS$_c$ model predictions are roughly the same as
the standard model and there are no considerable differences between the
predictions of these two models. In the case of differential decay rate, the
data in the range $4 $ GeV$^2/$c$^4\leq$ $q^2 \leq 6$ GeV$^2/$c$^4$ can not be
described by any of the considered models.
