We consider the intuitionistic fuzzification of $LI$-ideals in lattice implication algebras, called an intuitionistic fuzzy $LI$-ideal. We also mention the intuitionistic fuzzification of lattice ideals in a lattice, called an intuitionistic fuzzy lattice ideal, and discuss relationships between intuitionistic fuzzy $LI$-ideals and intuitionistic fuzzy lattice ideals. We establish some characterizations of intuitionistic fuzzy $LI$-ideals.