  We present a systematic study of $\Lambda_c^+ \to {\cal B}_q \ell^+ \nu_\ell
$ with ${\cal B}_q = (\Lambda, n)$ and $\ell =( e, \mu)$, examining all the
possible decay observables based on the homogeneous bag model (HBM) and lattice
QCD (LQCD). With the HBM, we find that the branching fractions and polarization
asymmetries of the daughter baryon $\Lambda$ are ${\cal B}(\Lambda_c^+ \to
\Lambda e^+ \nu_e, \Lambda \mu^+ \nu_\mu, n \ell ^+ \nu_\ell ) = (3.78 \pm
0.25, 3.67\pm 0.23, 0.40\pm 0.04 )\%$ and $\alpha_\Lambda (\Lambda_c^+ \to
\Lambda e^+ \nu_e,\Lambda\mu^+ \nu_\mu ) =(-82.6,-82.3)\%$, respectively. From
the LQCD, we obtain that $\alpha_{\Lambda}(\Lambda_c^+ \to \Lambda e^+ \nu_e,
\mu^+ \nu_\mu ) = (-87.4\pm 1.0,-87.2\pm 1.0)\%$. We also explore the
time-reversal asymmetries due to new physics beyond the standard model. All our
results are consistent with the current experimental data, while some of them
are accessible to the experiments at BESIII and Belle II.
