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We study the four body decay $\Lambda_b \rightarrow \Lambda ( \rightarrow p\pi^-) \mu^{+} \mu^{-}$ in the Randall-Sundrum model with custodial protection$(\text{RS}_c)$. By considering the constraints coming from the direct searchesof the lightest Kaluza-Klein (KK) excitation of the gluon, electroweakprecision tests, the measurements of the Higgs signal strengths at the LHC andfrom $\Delta F=2$ flavor observables, we perform a scan of the parameter spaceof the $\text{RS}_c$ model and obtain the maximum allowed deviations of theWilson coefficients $\Delta C^{(\prime)}_{7,\; 9,\; 10}$ for different valuesof the lightest KK gluon mass $M_{g^{(1)}}$. Later, their implications on theobservables such as differential branching fraction, longitudinal polarizationof the daughter baryon $\Lambda$, forward-backward asymmetry with respect toleptonic, hadronic and combined lepton-hadron angles are discussed where wepresent the analysis of these observables in different bins of di-muoninvariant mass squared $s\;(= q^2)$. It is observed that with the currentconstraints the Wilson coefficients in $\text{RS}_c$ model show slightdeviations from their Standard Model values and hence can not accommodate thediscrepancies between the Standard Model calculations of various observablesand the LHCb measurements in $\Lambda_b$ decays.

The $\Lambda_b \to \Lambda\ (\to p \pi^-)\mu^+\mu^-$ decay in the $\text{RS}_{c}$ model