  Let L be a restricted Lie superalgebra with its enveloping algebra u(L) over
a field F of characteristic p>2. A polynomial identity is called non-matrix if
it is not satisfied by the algebra of 2\times 2 matrices over F. We
characterize L when u(L) satisfies a non-matrix polynomial identity. In
particular, we characterize L when u(L) is Lie solvable, Lie nilpotent, or Lie
super-nilpotent.
