We study the semileptonic decays of $Lambda_c^+ to Lambda(n)ell^+ u_{ell}$ 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 ${cal B}( Lambda_c^+ to Lambda e^+ u_{e})=(3.36pm0.87,3.48)%$ and ${alpha}( Lambda_c^+ to Lambda e^+ u_{e})=(-0.97pm0.03,-0.83)$ in (LFCQM, MBM), in comparison with the data of ${cal B}( Lambda_c^+ to Lambda e^+ u_{e})=(3.6pm0.4)%$ and ${alpha}( Lambda_c^+ to Lambda e^+ u_{e})=-0.86pm 0.04$ given by the Particle Data Group, respectively. We also predict that ${cal B}( Lambda_c^+ to n e^+ u_{e})=(0.57pm0.15, 3.6pm1.5)times 10^{-3}$ and ${alpha}( Lambda_c^+ to n e^+ u_{e})=(-0.98pm0.02,-0.96pm0.04)$ in LFCQM with two different scenarios for the momentum distributions of quarks in the neutron, and ${cal B}( Lambda_c^+ to n e^+ u_{e})= 0.279times 10^{-2}$ and ${alpha}( Lambda_c^+ to n e^+ u_{e})=-0.87$ in MBM, which could be tested by the ongoing experiments at BESIII, LHCb and BELLEII.
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