Consider the matrix elements of L between two definite-parity states: (n''m'|L|nm). Under what conditions is this matrix

Consider the matrix elements of L̂ between two definite-parity states: (n'ℓ'm'|L̂|nℓm). Under what conditions is this matrix element guaranteed to vanish? Note that the same selection rule would apply to any pseudovector operator, or any “true” scalar operator.