Let \(ZG\) be the integral group ring of a group \(G\) and let \(\Delta^{(n)} (G)\) denote the \(n\)-th Lie power of the augmentation ideal \(\Delta (G)\) of \(ZG\). The intersection \(D_{(n)} (G) = G \cap (1 + \Delta^{(n)}(G))\) is known as the \(n\)-th Lie dimension subgroup of \(G\). The authors prove that for \(n = 7\) and \(n = 8\) the \(n\)-th Lie dimension subgroup \(D_{(n)} (G)\) coincides with the \(n\)-th lower central subgroup \(\gamma_ n(G)\) for any group \(G\). R. Sandling [J. Algebra 21, 216-231 (1972; Zbl 0233.20001)] has proved that \(D_{(n)}(G) = \gamma_ n(G)\) for \(n \leq 6\). On the other hand, T. C. Hurley and S. K. Sehgal [ibid. 143, 46-56 (1991; Zbl 0761.20003)] have shown that there exists a 2-group \(G\) such that \(D_{(n)} (G) \neq \gamma_ n(G)\) for \(n \geq 9\). Thus, this paper completely resolves the Lie dimension subgroup conjecture. Together with the known other results, this resolves also the restricted Lie dimension subgroup conjecture for all values of \(n\).