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Lagrangian matroids are a subclass of Coxeter matroids. These transversal matroids, introduced by Joseph Bonin (The George Washington University), are also known as symmetric matroids, $2$-matroids, and metroids. We define Lagrangian matroids and a special subclass of them, the so-called lattice path Lagrangian matroids. We also define lattice path matroids, which are not a subclass of lattice path Lagrangian matroids, but are instead a subclass of ordinary [unoriented] matroids. It is known that, given a transversal $T$ and any Lagrangian matroid $\mathcal{L}$, the collection $\mathcal{I}$ of sets that are mutually subsets of both $T$ and some basis of $\mathcal{L}$ is the set of independent sets of an ordinary matroid. Anna de Mier (Universitat Polit\`ecnica de Catalunya) asked if, in addition, requiring $\mathcal{L}$ is a lattice path Lagrangian matroid implies that the collection $\mathcal{I}$ is the set of independent sets of a \emph{lattice} path matroid. In this talk, we answer this question in the affirmative, and give the outline of an existential proof as well as an algorithm that constructs the bases of the lattice path matroid. The talk is entirely self-contained and does not require any knowledge of matroid theory. This is joint work with Anna Gundert (Freie Universit\"at Berlin) and Daria Schymura (Freie Universit\"at Berlin).