Abstract The notions of ILI-ideals in lattice implication algebras are introduced. Some relationships and characterizations of ILI-ideals in lattice implication algebras are studied. Furthermore,we discussed the extension theorems of ILI-ideals in lattice implication algebras. Finally, we proved that: (i) Every ILI-ideal of a lattice implication algebra is a lattice ideal conversely, in lattice H implication algebra; every lattice ideal is ILI-ideal. (ii) Every ILI-ideal of a latticeimplication algebra is a LI-ideal conversely, in a lattice H implicative algebra; every LI-ideal is a ILI-ideal.