  We present the first lattice-QCD determination of the form factors describing
the semileptonic decays $\Lambda_b \to \Lambda_c^*(2595)\ell^-\bar{\nu}$ and
$\Lambda_b \to \Lambda_c^*(2625)\ell^-\bar{\nu}$, where the $\Lambda_c^*(2595)$
and $\Lambda_c^*(2625)$ are the lightest charm baryons with $J^P=\frac12^-$ and
$J^P=\frac32^-$, respectively. These decay modes provide new opportunities to
test lepton flavor universality and also play an important role in global
analyses of the strong interactions in $b\to c$ semileptonic decays. We
determine the full set of vector, axial vector, and tensor form factors for
both decays, but only in a small kinematic region near the zero-recoil point.
The lattice calculation uses three different ensembles of gauge-field
configurations with $2+1$ flavors of domain-wall fermions, and we perform
extrapolations of the form factors to the continuum limit and physical pion
mass. We present Standard-Model predictions for the differential decay rates
and angular observables. In the kinematic region considered, the differential
decay rate for the $\frac12^-$ final state is found to be approximately 2.5
times larger than the rate for the $\frac32^-$ final state. We also test the
compatibility of our form-factor results with zero-recoil sum rules.
