Let \(A\) be a prime associative algebra over a commutative ring with \(1\), let \(L\) be a noncentral Lie ideal of \(A\) with center \(Z(L)\), and let \(\overline L=L/Z(L)\) be the factor Lie algebra. Under some mild technical assumptions (namely, \(\text{char}(A)\neq 2\) and \(A\) does not satisfy \(S_{14}\), the standard polynomial identity of degree 14) the authors describe the form of a Lie derivation \(\delta\) of \(\overline L\); roughly speaking, it is shown that \(\delta\) arises from a derivation of an associative subalgebra of \(A\) generated by \(L\). This result solves an old problem of Herstein. The proofs in this paper are based on functional identities. We remark that combining the recent achievements in the theory of functional identities with the classical results from the theory of polynomial identities, just recently \textit{K. I. Beidar}, \textit{M. Brešar}, \textit{M. A. Chebotar} and \textit{W. S. Martindale} gave complete answers to various of Herstein's Lie derivation questions [J. Algebra 238, No. 1, 239-264 (2001; Zbl 1019.16020) and ibid. 249, No. 1, 59-94 (2002; Zbl 1019.16021)].