In this paper, we introduce the concept of Fantastic LI-ideal and vague Fantastic LI-ideal of lattice implication Algebra. We prove that every fantastic LI ideal of lattice implication algebra L is a LI ideal of L and the converse need not be true. Then we give a condition LI ideal should be a fantastic LI ideal. Also we prove that ILI-ideals of lattice implication algebra are fantastic LIideals and fantastic LI-ideal need not to be ILI-ideal. Additionally, we give the extension property for fantastic LI-ideal. Finally, we apply the vague concept to the notion of fantastic LI-ideals and discussing relation among vague fantastic LI-ideals, vague LIideals and implicative LI-ideals and property of vague fantastic LI-ideals.