  We observe that embeddings into random metrics can be fruitfully used to
study the $L_1$-embeddability of lamplighter graphs or groups, and more
generally lamplighter metric spaces. Once this connection has been established,
several new upper bound estimates on the $L_1$-distortion of lamplighter
metrics follow from known related estimates about stochastic embeddings into
dominating tree-metrics. For instance, every lamplighter metric on a $n$-point
metric space embeds bi-Lipschitzly into $L_1$ with distortion $O(\log n)$. In
particular, for every finite group $G$ the lamplighter group $H =
\mathbb{Z}_2\wr G$ bi-Lipschitzly embeds into $L_1$ with distortion
$O(\log\log|H|)$. In the case where the ground space in the lamplighter
construction is a graph with some topological restrictions, better distortion
estimates can be achieved. Finally, we discuss how a coarse embedding into
$L_1$ of the lamplighter group over the $d$-dimensional infinite lattice
$\mathbb{Z}^d$ can be constructed from bi-Lipschitz embeddings of the
lamplighter graphs over finite $d$-dimensional grids, and we include a remark
on Lipschitz free spaces over finite metric spaces.
