  The interaction between $\Lambda_c$ and a nucleon ($N$) is investigated by
employing the HAL QCD method in the (2+1)-flavor lattice QCD on a
$(2.9~\mathrm{fm})^3$ volume at $m_\pi \simeq 410,~570,~700$ MeV. We study the
central potential in $^1S_0$ channel as well as central and tensor potentials
in $^3S_1 - $$^3D_1$ channel, and find that the tensor potential for $\Lambda_c
N$ is negligibly weak and central potentials in both $^1S_0$ and $^3S_1 -
$$^3D_1$ channels are almost identical with each other except at short
distances. Phase shifts and scattering lengths calculated with these potentials
show that the interaction of $\Lambda_c N$ system is attractive and has a
similar strength in $^1S_0$ and $^3S_1$ channels at low energies (i.e. the
kinetic energy less than about $40$ MeV). While the attractions are not strong
enough to form two-body bound states, our results lead to a possibility to form
$\Lambda_c$ hypernuclei for sufficiently large atomic numbers ($A$). To
demonstrate this, we derive a single-folding potential for $\Lambda_c$
hypernuclei from the $\Lambda_c$-nucleon potential obtained in lattice QCD, and
find that $\Lambda_c$ hypernuclei can exist for $A \ge 12$ with the binding
energies of a few MeV. We also estimate the Coulomb effect for the $\Lambda_c$
hypernuclei.
