Conditional Functional Dependencies (CFDs) are Functional Dependencies (FDs) that hold on a fragment relation of the original relation. In [17], the hierarchy between CFDs, association rules and some other dependencies have been shown.This paper exhibits the relation between CFDs and FCA. Given a many-valued relation we define a labeled lattice which gives a synthetic representation of the hierarchy of dependencies. Moreover, a formal concept in the nominal scaling of the relation is an instance of a closed set in the labeled lattice. Pure CFDs correspond to edges in this labeled lattice. We exhibit a monotone function on CFDs allowing search and pruning strategies. We also show that transitive edges induce redundant CFDs.