  A flat of a matroid is cyclic if it is a union of circuits; such flats form a
lattice under inclusion and, up to isomorphism, all lattices can be obtained
this way. A lattice is a Tr-lattice if all matroids whose lattices of cyclic
flats are isomorphic to it are transversal. We investigate some sufficient
conditions for a lattice to be a Tr-lattice; a corollary is that distributive
lattices of dimension at most two are Tr-lattices. We give a necessary
condition: each element in a Tr-lattice has at most two covers. We also give
constructions that produce new Tr-lattices from known Tr-lattices.
