  The heavy quark effective theory makes model independent predictions for
semileptonic $\Lambda_b \to \Lambda_c$ decays in terms of a small set of
parameters. No subleading Isgur-Wise function occurs at order $\Lambda_{\rm
QCD}/m_{c,b}$, and only two sub-subleading functions enter at order
$\Lambda_{\rm QCD}^2/m_c^2$. These features allow us to fit the form factors
and decay rates calculated up to order $\Lambda_{\rm QCD}^2/m_c^2$ to LHCb data
and lattice QCD calculations. We derive a significantly more precise standard
model prediction for the ratio ${\cal B}(\Lambda_b\to \Lambda_c \tau\bar\nu) /
{\cal B}(\Lambda_b\to \Lambda_c \mu\bar\nu)$ than prior results, and find the
expansion in $\Lambda_{\rm QCD}/m_c$ well-behaved, addressing a long-standing
question. Our results allow more precise and reliable calculations of
$\Lambda_b\to \Lambda_c\ell\bar\nu$ rates, and are systematically improvable
with better data on the $\mu$ (or $e$) modes.
