  For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among
other reasons, appeared as a means of constructing structures with lattices of
equivalence relations embedding $\Lambda$. This makes use of an isomorphism of
categories between $\Lambda$-ultrametric spaces and structures equipped with
certain families of equivalence relations. We extend this isomorphism to the
case of infinite lattices. We also pose questions about representing a given
finite lattice as the lattice of $\emptyset$-definable equivalence relations of
structures with model-theoretic symmetry properties.
