Throughout the review, \(R\) denotes a non-commutative prime ring of characteristic different from \(2\) with extended centroid \(C\). An additive map \(F\) of \(R\) into itself is called a generalized skew derivation of \(R\) if there exists a skew derivation \(d\) of \(R\) with associated automorphism \(\alpha\) such that \(F(xy)=F(x)y+\alpha (x)d(y)\) for any \(x,y\in R\). In the paper under review, the authors concentrate on the study of conditions that allow generalized skew derivations to preserve the Jordan product on Lie ideals of \(R\). More precisely, for a non-central Lie ideal \(L\) of \(R\) and a non-zero generalized skew derivation \(F\) of \(R\), the authors prove that if \((R(x)\circ F(y))^n=(x\circ y)^n\) for some \(n\geq 1\) and any \(x,y\in L\), then one of the following holds: (a) \(R\) satisfies \(s_4(x_1,\ldots,x_4)\), the standard polynomial identity on four non-commuting variables; (b) \(F(x)=\lambda x\) for some \(\lambda\in C\) such that \(\lambda^{2n}=1_C\) and for every \(x\in R\). The paper continues the work [F. Rania, Beitr. Algebra Geom. 60, No. 3, 513–525 (2019; Zbl 1437.16018); G. Scudo, “Jordan product preserving generalized skew derivations on Lie ideals”, Proceedings of International Conference of Algebra and Related Topics with Applications, ICARTA-19 (in press)].