Orthogonal subspace to subalgebra for Killing form not is subalgebra

Statement
It is possible to have a finite-dimensional Lie algebra $$L$$, and a Lie subalgebra $$S$$ of $$L$$, such that the orthogonal subspace $$S^\perp$$ to $$S$$ in $$L$$ with respect to the fact about::Killing form on $$L$$ is not a subalgebra.

Related facts

 * Orthogonal subspace to ideal for Killing form is ideal
 * Orthogonal subspace to derivation-invariant subalgebra for Killing form is derivation-invariant