  We develop a method to bound the dynamic asymptotic dimension of isometric
group actions $\Gamma\curvearrowright X$ in terms of the asymptotic dimension
of a space of graphs similar to a box space of $\Gamma$ (which also determines
finite-dimensionality), and a geometric property of $X$ related to the doubling
dimension. We apply this method to describe the DAD of translation actions by
finitely generated subgroups of compact Lie groups, characterize finite
dimensionality of such actions, and consequently bound the nuclear dimension of
$C^*$-algebras arising from such actions by amenable groups.
