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.