We investigate the exclusive semileptonic and nonleptonic ${\Lambda }_b\to {\Lambda }_c(p)$ decays within the Standard Model by using the light-front quark model. To determine the behavior of the ${\Lambda }_b\to {\Lambda }_c(p)$ transition form factors, we employ the Bethe-Salpeter formalism in the timelike region, effectively accounting for both valence and nonvalence contributions. Using these form factors, including nonvalence contributions, we obtain branching fractions of ${\Lambda }_b\to {\Lambda }_c\ell {\bar{\nu }}_{\ell }$, ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$, ${\Lambda }_b\to p\ell {\bar{\nu }}_{\ell }$ and ${\Lambda }_b\to p\tau {\bar{\nu }}_{\tau }$~($\ell =e$ or $\mu$) are found to be around $5.39\%$, $1.41\%$, $3.33\times {10}^{-4}$ and $2.08\times {10}^{-4}$, respectively, which are consistent with the experimental measurements. The ratios of $R^{\ell\tau}(\Lambda_{c})=\frac{{\cal B}({\Lambda_b}\to {\Lambda_c}\,\tau\,\bar{\nu}_\tau)} {{\cal B}({\Lambda_b}\to {\Lambda_c}\,\ell\,\bar{\nu}_l)}$ and $R^{\ell\tau}(p)=\frac{{\cal B}({\Lambda_b}\to p\,\tau\,\bar{\nu}_\tau)} {{\cal B}({\Lambda_b}\to p\,\ell\,\bar{\nu}_l)}$, are given by ${0.261}_{-0.117}^{+0.097}$ and ${0.624}_{-0.129}^{+0.119}$, respectively. The forward-backward asymmetries in the above semilepton decays are also examined. Our results indicate that, within the light-front framework, the nonvalence contributions to the asymmetries are negligible compared to the $\beta$-induced uncertainties. In addition, we calculate the branching ratios for the nonleptonic decays of ${\Lambda }_b\to {\Lambda }_c(p)M$ with $M$ being the pseudo scalar and vector mesons with the results found to be consistent with the current experimental data.