From the perspective that the $\Lambda_c(2595)$ and $\Lambda_c(2625)$ are dynamically generated resonances from the $DN,~D^*N$ interaction and coupled channels, we have evaluated the rates for $\Lambda_b \to \pi^- \Lambda_c(2595)$ and $\Lambda_b \to \pi^- \Lambda_c(2625)$ up to a global unknown factor that allows us to calculate the ratio of rates and compare with experiment, where good agreement is found. Similarly, we can also make predictions for the ratio of rates of the, yet unknown, decays of $\Lambda_b \to D_s^- \Lambda_c(2595)$ and $\Lambda_b \to D_s^- \Lambda_c(2625)$ and make estimates for their individual branching fractions.
We evaluate the partial decay widths for the semileptonic $\Lambda_b \to \bar \nu_l l \Lambda_c(2595)$ and $\Lambda_b \to \bar \nu_l l \Lambda_c(2625)$ decays from the perspective that these two $\Lambda^*_c$ resonances are dynamically generated from the $DN$ and $D^*N$ interaction with coupled channels. We find that the ratio of the rates obtained for these two reactions is compatible with present experimental data and is very sensitive to the $D^* N$ coupling, which becomes essential to obtain agreement with experiment. Together with the results obtained for the $\Lambda_b \to \pi^- \Lambda^*_c$ reactions, it gives strong support to the molecular picture of the two $\Lambda^*_c$ resonances and the important role of the $D^*N$ component neglected in prior studies of the $\Lambda_c(2595)$ from the molecular perspective.