In this paper we introduce the notion of an intuitionistic (S,T)-fuzzy Lie ideal of a Lie algebra and investigate some related properties. Nilpotency of intuitionistic (S,T)-fuzzy Lie ideals is introduced. Intuitionistic (S,T)-fuzzy of adjoint representation of Lie algebras is introduced and the relation between this representation and nilpotent intuitionistic (S,T)-fuzzy Lie ideals is discussed. Killing form in the intuitionistic (S,T)-fuzzy case is defined and some of its properties are studied.