  We study the $\Lambda_c N$ interaction in the covariant chiral effective
field theory (ChEFT) at leading order. All the relevant low-energy constants
are determined by fitting to the lattice QCD simulations from the HAL QCD
Collaboration. Extrapolating the results to the physical point, we show that
the $\Lambda_c N$ interaction is weakly attractive in the $^1S_0$ channel, but
in the $^3S_1$ channel, it is only attractive at extremely low energies and
soon turns repulsive for larger laboratory energy. Furthermore, we show that
the neglect of the $^3S_1-{}^3D_1$ coupling provided by the leading order
covariant ChEFT would result in an attractive interaction in the $^3S_1$
channel at the physical point, which coincides with the previous non-relatistic
ChEFT study. As a byproduct, we predict the $^3D_1$ phase shifts and the mixing
angel $\varepsilon_1$, which can be checked by future lattice QCD simulations.
In addition, we compare the $\Lambda_c N$ interaction with the $\Lambda N$ and
$NN$ interactions to study how the baryon-nucleon ($BN$) interactions evolve as
a function of the baryon mass with the replacement of a light quark by a
strange or charm quark in the baryon ($B$).
