\begin{document}$ \Lambda_b $\end{document} decaying into \begin{document}$ \Lambda_c $\end{document} within the framework of light-cone sum rules with the distribution amplitudes (DAs) of the \begin{document}$ \Lambda_b $\end{document}-baryon. In the hadronic representation of the correlation function, we isolate both the \begin{document}$ \Lambda_c $\end{document} and \begin{document}$ \Lambda_c^* $\end{document} states so that the \begin{document}$ \Lambda_b \rightarrow \Lambda_c $\end{document}form factors can be obtained without ambiguity. We investigate the P-type and A-type currents to interpolate light baryons for comparison because the interpolation current for the baryon state is not unique. We also employ three parametrization models for the DAs of \begin{document}$ \Lambda_b $\end{document} in the numerical calculation. We present the numerical predictions for the \begin{document}$ \Lambda_b \rightarrow \Lambda_c $\end{document} form factors and branching fractions, averaged forward-backward asymmetry, averaged final hadron polarization, and averaged lepton polarization of the \begin{document}$ \Lambda_b \to \Lambda_c \ell\mu $\end{document} decays, as well as the ratio of the branching ratios \begin{document}$ R_{\Lambda_c} $\end{document}. The predicted \begin{document}$ R_{\Lambda_c} $\end{document} is consistent with LHCb data."> Λ<sub><i>b</i></sub> → Λ<sub><i>c</i></sub> form factors from QCD light-cone sum rules -
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