  In this paper, we study the sharp Poincar\'e inequality and the Sobolev
inequalities in the higher order Lorentz--Sobolev spaces in the hyperbolic
spaces. These results generalize the ones obtained in \cite{Nguyen2020a} to the
higher order derivatives and seem to be new in the context of the
Lorentz--Sobolev spaces defined in the hyperbolic spaces.

Functional Analysis