  The semi-leptonic decays of $\Lambda_{b}\to\Lambda_{c}^{(*)}\ell\nu_\ell$ and
$\Lambda_{c}\to\Lambda^{(*)}\ell\nu_\ell$ are studied in the light-front quark
model in this work. Instead of the quark-diquark approximation, we use the
three-body wave functions obtained by the involving baryon spectroscopy. The
ground states $(1/2^{+})$, the $\lambda$-mode orbital excited states
$(1/2^{-})$ and the first radial excited states $(1/2^{+})$ of
$\Lambda_{(c)}^{(*)}$ are considered. The discussions are given for the form
factors, partial widths, branching fractions, leptonic forward-backward
asymmetries, hadron polarizations, lepton polarizations, and the lepton flavor
universalities. Our results are useful for the inputs of heavy baryon decays
and understanding the baryon structures, and helpful for the experimental
measurements.
