Let
$R$ be a non-
$\text{GPI}$ prime ring with involution and characteristic
$\ne 2,3$. Let
$K$ denote the skew elements of
$R$, and
$C$ denote the extended centroid of
$R$. Let
$\delta$ be a Lie derivation of
$K$ into itself. Then
$\delta \,=\,\rho \,+\,\varepsilon$ where
$\varepsilon$ is an additive map into the skew elements of the extended centroid of
$R$ which is zero on
$\left[ K,\,K \right]$, and
$\rho$ can be extended to an ordinary derivation of
$\left\langle K \right\rangle$ into
$RC$, the central closure.