  Understanding the properties of the strange $\Lambda^*$ baryon resonances is
a long-standing and fascinating problem. $\Lambda_c$ charm-baryon semileptonic
weak decays to these resonances are highly sensitive to their internal
structure and can be used to test theoretical models. We have performed the
first lattice-QCD computation of the form factors governing $\Lambda_c$
semileptonic decays to a $\Lambda^*$ resonance: the $\Lambda^*(1520)$, which
has negative parity and spin $3/2$. Here we present the resulting
Standard-Model predictions of the $\Lambda_c\to\Lambda^*(1520)\ell^+\nu_\ell$
differential and integrated decay rates as well as angular observables.
Furthermore, by combining the recent BESIII measurement of the $\Lambda_c \to X
e^+ \nu_e$ inclusive semipositronic branching fraction [Phys. Rev. Lett. 121,
251801 (2018)] with lattice-QCD predictions of the $\Lambda_c \to \Lambda e^+
\nu_e$, $\Lambda_c \to n e^+ \nu_e$, and $\Lambda_c \to \Lambda^*(1520) e^+
\nu_e$ decay rates, we obtain an upper limit on the sum of the branching
fractions to all other semipositronic final states. In particular, this upper
limit constrains the $\Lambda_c\to\Lambda^*(1405)e^+ \nu_e$ branching fraction
to be very small, which may be another hint for a molecular structure of the
$\Lambda^*(1405)$.
