  We prove that $\delta$-derivations of a simple finite-dimensional Lie algebra
over a field of characteristic zero, with values in a finite-dimensional
module, are either inner derivations, or, in the case of adjoint module,
multiplications by a scalar, or some exceptional cases related to
$\mathfrak{sl}(2)$. This can be viewed as an extension of the classical first
Whitehead Lemma.
