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.
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