  In terms of ${\cal P}_{c1,c2}={\cal P}_c(4380,4450)^+$ as the hidden charm
pentaquark states to consist of $c\bar c uud$, we study the semileptonic
$\Lambda_b\to ({\cal P}_{c1,c2}\to)J/\psi p \ell^-\bar \nu_\ell$ decays. In our
discussion, while the main contribution to $\Lambda_b\to K^-J/\psi p$ is from
the non-perturbative process via the doubly charmful $b\to c\bar cs$
transition, we propose that the $\Lambda_b\to {\cal P}_{c1,c2}\to J/\psi p$
transitions are partly contribute to the $\Lambda_b\to K^-({\cal
P}_{c1,c2}\to)J/\psi p$ decays, in which the required $c\bar c$ pair is formed
by the sea quarks, intrinsic charm, or both. We predict that ${\cal
B}(\Lambda_b\to J/\psi p \ell^-\bar
\nu_\ell)=(2.04^{+4.82}_{-1.57},1.75^{+4.14}_{-1.35})\times 10^{-6}$ for
$\ell=(e,\mu)$, which are about two orders of magnitude smaller than the
observed decay of $\Lambda_b\to p\mu\bar \nu_\mu$. We also explore the angular
correlations for the $J/\psi p$ and $\ell^-\bar \nu_\ell$ pairs. Our results of
the decay branching ratios and angular asymmetries in $\Lambda_b\to J/\psi p
\ell^-\bar \nu_\ell$, accessible to the ongoing experiments at the LHCb, can be
used to improve the understanding of the hidden charm pentaquark states.
