We have studied the nonleptonic $\Lambda_b \to \pi^- (D_s^-) \Lambda_c^*$ and the semileptonic $\Lambda_b \to \bar \nu_l l \Lambda_c^*$ decays, with $\Lambda^*_c \equiv \Lambda_c(2595), \Lambda_c(2625)$, from the perspective that the two $\Lambda^*_c$ resonances are dynamically generated from the $DN, D^*N$ interaction with coupled channels. We have developed a formalism to relate the $\Lambda_b \to \pi^- DN$ and $\Lambda_b \to \pi^- D^*N$ decays. We can evaluate the rates for these transitions, up to a global unknown factor. We find that the ratios of the rates obtained for these reactions are compatible with present experimental data and are very sensitive to the $D^* N$ coupling, which becomes essential to obtain agreement with experiment. The results obtained with these reactions give support to the molecular picture for these two $\Lambda^*_c$ resonances. Work with other models and checks for further experiments will help us gain further insight on the nature of these resonances, and new experiments producing these two resonances should be encouraged.