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 $Lambda_ctoLambda^*(1520)ell^+ u_ell$ differential and integrated decay rates as well as angular observables. Furthermore, by combining the recent BESIII measurement of the $Lambda_c to X e^+ u_e$ inclusive semipositronic branching fraction [Phys. Rev. Lett. 121, 251801 (2018)] with lattice-QCD predictions of the $Lambda_c to Lambda e^+ u_e$, $Lambda_c to n e^+ u_e$, and $Lambda_c to Lambda^*(1520) e^+ u_e$ 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 $Lambda_ctoLambda^*(1405)e^+ u_e$ branching fraction to be very small, which may be another hint for a molecular structure of the $Lambda^*(1405)$.
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