  We study the semileptonic decays of $\Lambda_c^+ \to \Lambda(n)\ell^+
\nu_{\ell}$ in two relativistic dynamical approaches of the light-front
constituent quark model (LFCQM) and MIT bag model (MBM). By considering the
Fermi statistic between quarks and determining spin-flavor structures in
baryons along with the helicity formalism in the two different dynamical
models, we calculate the branching ratios (${\cal B}$s) and averaged asymmetry
parameters ($\alpha$s) in the decays. Explicitly, we find that ${\cal B}(
\Lambda_c^+ \to \Lambda e^+ \nu_{e})=(3.36\pm0.87,3.48)\%$ and ${\alpha}(
\Lambda_c^+ \to \Lambda e^+ \nu_{e})=(-0.97\pm0.03,-0.83)$ in (LFCQM, MBM), in
comparison with the data of ${\cal B}( \Lambda_c^+ \to \Lambda e^+
\nu_{e})=(3.6\pm0.4)\%$ and ${\alpha}( \Lambda_c^+ \to \Lambda e^+
\nu_{e})=-0.86\pm 0.04$ given by the Particle Data Group, respectively. We also
predict that ${\cal B}( \Lambda_c^+ \to n e^+ \nu_{e})=(0.57\pm0.15,
3.6\pm1.5)\times 10^{-3}$ and ${\alpha}( \Lambda_c^+ \to n e^+
\nu_{e})=(-0.98\pm0.02,-0.96\pm0.04)$ in LFCQM with two different scenarios for
the momentum distributions of quarks in the neutron, and ${\cal B}( \Lambda_c^+
\to n e^+ \nu_{e})= 0.279\times 10^{-2}$ and ${\alpha}( \Lambda_c^+ \to n e^+
\nu_{e})=-0.87$ in MBM, which could be tested by the ongoing experiments at
BESIII, LHCb and BELLEII.
