  In the context of lepton flavor universality violation (LFUV) studies, we
fully derive a general tensor formalism to investigate the role that left- and
right-handed neutrino new-physics (NP) terms may have in $b\to c
\tau\bar\nu_\tau$ transitions. We present, for several extensions of the
Standard Model (SM), numerical results for the
$\Lambda_b\to\Lambda_c\tau\bar\nu_\tau$ semileptonic decay, which is expected
to be measured with precision at the LHCb. This reaction can be a new source of
experimental information that can help to confirm, or maybe rule out, LFUV
presently seen in $\bar B$ meson decays. The present study analyzes observables
that can help in distinguishing between different NP scenarios that otherwise
provide very similar results for the branching ratios, which are our currently
best hints for LFUV. Since the $\tau$ lepton is very short-lived, we consider
three subsequent $\tau$-decay modes, two hadronic $\pi\nu_\tau$ and
$\rho\nu_\tau$ and one leptonic $\mu\bar\nu_\mu\nu_\tau$, which have been
previously studied for $\bar B\to D^{(*)}$ decays. Within the tensor formalism
that we have developed in previous works, we re-obtain the expressions for the
differential decay width written in terms of visible (experimentally
accessible) variables of the massive particle created in the $\tau$ decay.
There are seven different $\tau$ angular and spin asymmetries that are defined
in this way and that can be extracted from experiment. Those asymmetries
provide observables that can help in constraining possible SM extensions.
