Let a be a letter of an alphabet A. Given a lattice of languages L, we describe the set of ultrafilter inequalities satisfied by the lattice La generated by the languages of the form L or LaA * , where L is a language of L. We also describe the ultrafilter inequalities satisfied by the lattice L1 generated by the lattices La, for a ∈ A. When L is a lattice of regular languages, we first describe the profinite inequalities satisfied by La and L1 and then provide a small basis of inequalities defining L1 when L is a Boolean algebra of regular languages closed under quotient.