  We study $S$-wave interactions in the
$I\left(J^{p}\right)=1/2\left(1/2^{-}\right)$ $\Lambda_{c}K^{+}-pD_{s}$ system
on the basis of the coupled-channel HAL QCD method. The potentials which are
faithful to QCD S-matrix below the $ pD^{*} $ threshold are extracted from
Nambu-Bethe-Salpeter wave functions on the lattice in Flavor $
\textrm{SU}\left(3\right) $ Limit. For the simulation, we employ $ 3 $-flavor
full QCD gauge configurations on a $\left(1.93 \:\textrm{fm} \right)^{3}$
volume at $m_{\pi}\simeq 872$ MeV. %\textcolor{red}{For the charm quark, the
relativistic heavy quark action is employed to treat its dynamics on the
lattice}.
  We present our results of the S-wave coupled-channel potentials for the
$\Lambda_{c}K^{+}-pD_{s}$ system in the $1/2\left(1/2^{-}\right)$ state as well
as scattering observables obtained from the extracted potential matrix. We
observe that the coupling between $\Lambda_{c}K^{+}$ and $pD_{s}$ channels is
weak. The phase shifts and scattering length obtained from the extracted
potential matrix show that the $\Lambda_{c}K^{+}$ interaction is attractive at
low energy and stronger than the $pD_{s}$ interaction though no bound state at
$m_{\pi}\geq872$ MeV.
