  We continue with the study of octahedral norms in the context of spaces of
Lipschitz functions and in their duals. First, we prove that the norm of
$\mathcal F(M)^{**}$ is octahedral as soon as $M$ is unbounded or is not
uniformly discrete. Further, we prove that a concrete sequence of uniformly
discrete and bounded metric spaces $(K_m)$ satisfies that the norm of $\mathcal
F(K_m)^{**}$ is octahedral for every $m$. Finally, we prove that if $X$ is an
arbitrary Banach space and the norm of $\operatorname{Lip}_0(M)$ is octahedral,
then the norm of $\operatorname{Lip}_0(M,X^\ast)$ is octahedral. These results
solve several open problems from the literature.
