  Let $\mathfrak{g}$ be a real finite-dimensional Lie algebra containing
pointed generating invariant closed convex cones. We determine those
derivations $D$ of $\mathfrak{g}$ which induce a 3-grading of the form
$\mathfrak{g} = \mathfrak{g}_{-1} \oplus \mathfrak{g}_0 \oplus \mathfrak{g}_1$
on $\mathfrak{g}$ such that the $(\pm 1)$-eigenspaces $\mathfrak{g}_{\pm 1}$ of
$D$ are generated by the intersections with generating cones of the form $W =
\mathcal{O}_f^*$, where $\mathcal{O}_f$ is the coadjoint orbit of a linear
functional $f \in \mathfrak{z}(\mathfrak{g})^*$ and $\mathcal{O}_f^*$ is the
dual cone of $\mathcal{O}_f$. In particular, we show that, if $\mathfrak{g}$ is
solvable, no such derivation except the trivial one exists.
  This continues our classification of Lie algebras generated by Lie wedges of
endomorphism semigroups of standard subspaces. The classification is motivated
by the relation of nets of standard subspaces to Haag-Kastler nets of von
Neumann algebras in Algebraic Quantum Field Theory.
