  We report a branching fraction measurement of the singly Cabibbo-suppressed
decay $\Lambda_{c}^{+}\to\Lambda K^{+}$ using a data sample collected with the
BESIII detector at the BEPCII storage ring. The data span center-of-mass
energies from 4.599 to 4.950 GeV and correspond to an integrated luminosity of
6.44 fb$^{-1}$. The branching fraction of $\Lambda_{c}^{+}\to\Lambda K^{+}$
relative to that of the Cabibbo-favored decay $\Lambda_{c}^{+}\to\Lambda
\pi^{+}$ is measured to be
$\mathcal{R}=\frac{\mathcal{B}(\Lambda_{c}^{+}\to\Lambda
K^{+})}{\mathcal{B}(\Lambda_{c}^{+}\to\Lambda
\pi^{+})}=(4.78\pm0.34\pm0.20)\%$. Combining with the world-average value of
$\mathcal{B}(\Lambda_{c}^{+}\to\Lambda \pi^{+})$, we obtain
$\mathcal{B}(\Lambda_c^+\to\Lambda K^+)=(6.21\pm0.44\pm0.26\pm0.34)\times
10^{-4}$. Here the first uncertainties are statistical, the second systematic,
and the third comes from the uncertainty of the $\Lambda_{c}^{+}\to\Lambda
\pi^{+}$ branching fraction. This result, which is more precise than previous
measurements, does not agree with theoretical predictions, and suggests that
non-factorizable contributions have been under-estimated in current models.
