Summary: H. E. Bell and L. C. Kappe [Acta Math. Hung. 53, No. 3/4, 339-346 (1989; Zbl 0705.16021), Theorem 3] proved that if \(d\) is a derivation of a prime ring \(R\) which acts as a homomorphism or an anti-homomorphism on a nonzero right ideal \(I\) of \(R\), then \(d=0\) on \(R\). In the present paper our objective is to extend this result to Lie ideals. The following result is proved: Let \(R\) be a 2-torsion free prime ring and \(U\) a nonzero Lie ideal of \(R\) such that \(u^2\in U\), for all \(u\in U\). If \(d\) is a derivation of \(R\) which acts as a homomorphism or an anti-homomorphism on \(U\), then either \(d=0\) or \(U\subseteq Z(R)\).