  We study Jordan 3-graded Lie algebras satisfying 3-graded polynomial
identities. Taking advantage of the Tits-Kantor-Koecher construction, we
interpret the PI condition in terms of their associated Jordan pairs, which
allows us to formulate an analogous of Posner-Rowen Theorem for strongly prime
PI Jordan 3-graded Lie algebras. Arbitrary PI Jordan 3-graded Lie algebras are
also described by introducing the Kostrikin radical of the Lie algebras.
