In this article we deal with the free Banach lattice F B L ⟨ L ⟩ FBL\langle \mathbb {L} \rangle generated by a lattice L \mathbb {L} . We prove that if F B L ⟨ L ⟩ FBL\langle \mathbb {L} \rangle is projective then L \mathbb {L} has a maximum and a minimum. On the other hand, we show that if L \mathbb {L} has maximum and minimum then F B L ⟨ L ⟩ FBL\langle \mathbb {L} \rangle is 2 2 -lattice isomorphic to a C ( K ) C(K) -space. As a consequence, F B L ⟨ L ⟩ FBL\langle \mathbb {L} \rangle is projective if and only if it is lattice isomorphic to a C ( K ) C(K) -space with K K being an absolute neighborhood retract. As an application, we characterize those linearly ordered sets and Boolean algebras for which the corresponding free Banach lattice is projective.