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The first lattice QCD calculation of the form factors governing $\Lambda_c\to \Lambda \ell^+ \nu_\ell$ decays is reported. The calculation was performedwith two different lattice spacings and includes one ensemble with a pion massof 139(2) MeV. The resulting predictions for the $\Lambda_c \to \Lambda e^+\nu_e$ and $\Lambda_c \to \Lambda \mu^+ \nu_\mu$ decay rates divided by$|V_{cs}|^2$ are $0.2007(71)(74)\:{\rm ps}^{-1}$ and $0.1945(69)(72)\:{\rmps}^{-1}$, respectively, where the two uncertainties are statistical andsystematic. Taking the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ froma global fit and the $\Lambda_c$ lifetime from experiments, this translates tobranching fractions of $\mathcal{B}(\Lambda_c\to\Lambdae^+\nu_e)=0.0380(19)_{\rm LQCD\:\:}(11)_{\tau_{\Lambda_c}}$ and$\mathcal{B}(\Lambda_c\to\Lambda \mu^+\nu_\mu)=0.0369(19)_{\rmLQCD\:\:}(11)_{\tau_{\Lambda_c}}$. These results are consistent with, and twotimes more precise than, the measurements performed recently by the BESIIICollaboration. Using instead the measured branching fractions together with thelattice calculation to determine the CKM matrix element gives $|V_{cs}|=0.949(24)_{\rm LQCD\:\:}(14)_{\tau_{\Lambda_c}}(49)_{\mathcal{B}}$.

$\Lambda_c \to \Lambda \ell^+ \nu_\ell$ form factors and decay rates from lattice QCD with physical quark masses