  Form factors of the rare $\Lambda_{b}(\Lambda_{b}^*)\to N\ell^{+}\ell^{-}$
decays are calculated in the framework of the light cone QCD sum rules by
taking into account of the contributions from the negative parity baryons.
Using the obtained results on the form factors, the branching ratios of the
considered decays are estimated. The numerical survey for the branching ratios
of the $\Lambda_b \rar N\ell^+\ell^- $ and $\Lambda_b^\ast \rar N\ell^+\ell^- $
decays indicate that these transitions could be measurable in LHCb in near
future. Comparison of our predictions on the form factors and branching ratios
with those existing in the literature is also performed.
