$\mathrm{\Lambda }$-ultrametric spaces and lattices of equivalence relations

For a finite lattice $\mathrm{\Lambda }$, $\mathrm{\Lambda }$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\mathrm{\Lambda }$. This makes use of an isomorphism of categories between $\mathrm{\Lambda }$-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 $\mathrm{\varnothing }$-definable equivalence relations of structures with model-theoretic symmetry properties.