Abstract In this project work, the notions of weak LI-ideals and maximal weak LI-ideals of lattice implication algebras are introduced, respectively. The properties of WLI-ideals are investigated. Some relationships and characterizations of WLI-ideals in lattice implication algebras are studied. Furthermore, this project discussed about the extension theorems of LI-ideals in lattice implication algebras. And prove that (1) Every ILI-ideal of a lattice implication algebra is WLI-ideal. (2) Every lattice ideal in lattice H implication algebra is WLI-ideal.