Some operation on lattice implication algebras was introduced by Roh et al. [5]. In this project work, we introduce the concept of homomorphisms in lattice implication algebras, a ⊗-closed set and a ⊗-homomorphism in lattice implication algebras, and we discuss some of their properties. By using a counter example, we disprove a result in Roh et al. [5] about the properties a ⊗-closed set. Next, we introduce fuzzy filter and fuzzy implicative filter in lattice implication algebras, and obtain equivalent conditions. Finally, we discuss the operation ⊗ on fuzzy filters and fuzzy implicative filter in lattice implication algebras.