  In recent times, several hints of lepton non-universality have been observed
in semileptonic $B$ meson decays, both in the charged-current ($b \to c l \bar
\nu_l$) and neutral-current ($b \to s ll $) transitions. Motivated by these
intriguing results, we perform a model independent analysis of the semileptonic
$\Lambda_b$ decays involving the quark level transitions $b \to (u,c) l \nu_l$,
in order to scrutinize the nature of new physics. We constrain the new
parameter space by using the measured branching ratios of $B_{c, u}^+ \to
\tau^+ \nu_\tau$, $B \to \pi \tau \nu_\tau$ processes and the existing
experimental results on $R_{D^{(*)}}$, $R_{J/\psi}$ and $R_{\pi}^l$ parameters.
Using the constrained parameters, we estimate the branching ratios, forward
backward asymmetries, hadron and lepton polarization asymmetries of the
$\Lambda_b \to (\Lambda_c, p) l \nu_l$ processes. Moreover, we also examine
whether there could be any lepton universality violation in these decay modes.
