  Let $K$ be a field and $\Gamma$ a finite quiver without oriented cycles. Let
$\Lambda$ be the path algebra $K(\Gamma, \rho)$ and let $\mathscr{D}(\Lambda)$
be the dual extension of $\Lambda$. In this paper, we prove that each Lie
derivation of $\mathscr{D}(\Lambda)$ is of the standard form.
