  We provide new examples of translation actions on locally compact groups with
the "local spectral gap property" introduced in \cite{BISG15}. This property
has applications to strong ergodicity, the Banach-Ruziewicz problem, orbit
equivalence rigidity, and equidecomposable sets. The main group of study here
is the group $\text{Isom}(\mathbb{R}^d)$ of orientation-preserving isometries
of the euclidean space $\mathbb{R}^d$, for $d \geq 3$. We prove that the
translation action of a countable dense subgroup $\Gamma$ on Isom$(\mathbb
R^d)$ has local spectral gap, whenever the translation action of the rotation
projection of $\Gamma$ on $\text{SO}(d)$ has spectral gap. Our proof relies on
the amenability of $\text{Isom}(\mathbb{R}^d)$ and on work of Lindenstrauss and
Varj\'u, \cite{LV14}.
