  The category of complete differential graded Lie algebras provides nice
algebraic models for the rational homotopy types of non-simply connected
spaces. In particular, there is a realization functor, $\langle -\rangle$, of
any complete differential graded Lie algebra as a simplicial set. In a previous
article, we considered the particular case of a complete graded Lie algebra,
$L_{0}$, concentrated in degree 0 and proved that $\langle L_{0}\rangle$ is
isomorphic to the usual bar construction on the Malcev group associated to
$L_{0}$.
  Here we consider the case of a complete differential graded Lie algebra,
$L=L_{0}\oplus L_{1}$, concentrated in degrees 0 and 1. We establish that the
category of such two-stage Lie algebras is equivalent to explicit subcategories
of crossed modules and Lie algebra crossed modules, extending the equivalence
between pronilpotent Lie algebras and Malcev groups. In particular, there is a
crossed module $\mathcal{C}(L)$ associated to $L$. We prove that
$\mathcal{C}(L)$ is isomorphic to the Whitehead crossed module associated to
the simplicial pair $(\langle L\rangle, \langle L_{0}\rangle)$. Our main result
is the identification of $\langle L\rangle$ with the classifying space of
$\mathcal{C}(L)$.
