In this paper, we study distributive lattices for use in Formal Concept Analysis (FCA). Principal motivation comes from phylogeny and median graphs, to represent biological derivations and parcimonious trees. FCA proposes efficient algorithms to build concept lattices. Nevertheless, a concept lattice is not in correspondence with a median graph, except if it is a distributive one, hence comes the idea to study how to transform a concept lattice in a distributive one. In goal to achieve it, we use Birkhoff representation theorem, which allows to compute the transformation of any context in the context of a distributive lattice. So, we can use all the FCA algorithmic to build but also visualise distributive concept lattices, and to study associated median graphs.