The notion of IFI−ideal is introduced in lattice implication algebras. Firstly, the equivalent conditions of IF−ideals and IFI−ideals are given in lattice implication algebras. Then the proposition of IFI−ideal is investigated in lattice implication algebras. Next, the relations between IFI−ideal and IF−ideal, between IFI−ideal and IFI−filter, between IFI−ideal and fuzzy impilcative ideals, between IFI−ideal and implicative ideals are discussed in lattice implication algebras. Moreover, the extension theorem of IFI−ideals is obtained, and Ψ(L) which is composed of all IFI−ideals constitutes a closure system. Finally, we prove that ∀α ∈ [0, 1], A = (µ 0,α , µ 0,α ) is an IFI−ideal of lattice implication algebra L if and only if L is a lattice H implication algebra.