  The absolute branching fraction of $\Lambda \to p \mu^- \bar{\nu}_{\mu}$ is
reported for the first time based on an $e^+e^-$ annihilation sample of ten
billion $J/\psi$ events collected with the BESIII detector at $\sqrt{s}=3.097$
GeV. The branching fraction is determined to be ${\mathcal B}(\Lambda \to
p\mu^- \bar{\nu}_{\mu}) = [1.48\pm0.21(\rm stat) \pm 0.08(\rm syst)]\times
10^{-4}$, which is a significant improvement in precision over the previous
indirect measurements. Combining this result with the world average of
${\mathcal B}(\Lambda \to p e^- \bar{\nu}_{e})$, we obtain the ratio,
$\frac{\Gamma(\Lambda \to p \mu^- \bar{\nu}_{\mu})}{\Gamma(\Lambda \to p e^-
\bar{\nu}_{e})}$, to be $0.178 \pm 0.028$, which agrees with the standard model
prediction assuming lepton flavor universality. The asymmetry of the branching
fractions of $\Lambda \to p \mu^- \bar{\nu}_{\mu}$ and $\bar{\Lambda} \to
\bar{p} \mu^+ \nu_{\mu}$ is also determined, and no evidence for $CP$ violation
is found.
