Lie identities on enveloping algebras of restricted Lie superalgebras

Let L   be a restricted Lie superalgebra with its restricted enveloping algebra u(L)u(L) over a field FF of characteristic p>2p>2. Then u(L)u(L) can be viewed both as a Lie algebra and a Lie superalgebra. We characterize L   when u(L)u(L) is Lie solvable, Lie nilpotent, or Lie super-nilpotent.