  We present, for the first time, the six-fold differential decay density
expression for $\Lambda^0_b\to\Lambda^+_{c} l^- \bar{\nu}_{l}$, taking into
account the polarisation of the $\Lambda^0_b$ baryon and a complete basis of
new physics operators. Using the expected yield in the current dataset
collected at the LHCb experiment, we present sensitivity studies to determine
the experimental precision on the Wilson coefficients of the new physics
operators with $\Lambda^0_{b}\to\Lambda^+_{c}\mu^{-}\bar{\nu}_{\mu}$ decays in
two scenarios. In the first case, unpolarised
$\Lambda^0_{b}\to\Lambda^+_{c}\mu^{-}\bar{\nu}_{\mu}$ decays with
$\Lambda^+_c\to p K^+ \pi^-$ are considered, whereas polarised
$\Lambda^0_{b}\to\Lambda^+_{c}\mu^{-}\bar{\nu}_{\mu}$ decays with $\Lambda^+_c
\to p K^0_S$ are studied in the second. For the latter scenario, the
experimental precision that can be achieved on the determination of
$\Lambda^0_b$ polarisation and $\Lambda^+_c$ weak decay asymmetry parameter is
also presented.
