  A group is LERF (locally extended residually finite) if all its finitely
generated subgroups are separable. We prove that the trialitarian arithmetic
lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result,
together with previous work by the third author, implies that all arithmetic
lattices in $\mathbf{PO}_{n,1}(\mathbb{R})$, $n>3$, are not LERF.
