  Diestel-Leader graphs are neither hyperbolic nor CAT(0), so their visual
boundaries may be pathological. Indeed, we show that for $d>2$,
$\partial\text{DL}_d(q)$ carries the indiscrete topology. On the other hand,
$\partial\text{DL}_2(q)$, while not Hausdorff, is $T_1$, totally disconnected,
and compact. Since $\text{DL}_2(q)$ is a Cayley graph of the lamplighter group
$L_q$, we also obtain a nice description of $\partial\text{DL}_2(q)$ in terms
of the lamp stand model of $L_q$ and discuss the dynamics of the action.
