We consider the universal sector of a \(d\)-dimensional large-\(N\) strongly-interacting holographic CFT on a black hole spacetime background \(B\). When our CFT\(_d\) is coupled to dynamical Einstein-Hilbert gravity with Newton constant \(G_{d}\), the combined system can be shown to satisfy a version of the thermodynamic Generalized Second Law (GSL) at leading order in \(G_{d}\). The quantity \(S_{CFT} + \frac{A(H_{B, \text{perturbed}})}{4G_{d}}\) is non-decreasing, where \(A(H_{B, \text{perturbed}})\) is the (time-dependent) area of the new event horizon in the coupled theory. Our \(S_{CFT}\) is the notion of (coarse-grained) CFT entropy outside the black hole given by causal holographic information -- a quantity in turn defined in the AdS\(_{d+1}\) dual by the renormalized area \(A_{ren}(H_{\rm bulk})\) of a corresponding bulk causal horizon. A corollary is that the fine-grained GSL must hold for finite processes taken as a whole, though local decreases of the fine-grained generalized entropy are not obviously forbidden. Another corollary, given by setting \(G_{d} = 0\), states that no finite process taken as a whole can increase the renormalized free energy \(F = E_{out} - T S_{CFT} - \Omega J - \Phi Q\), with \(T, \Omega, \Phi\) constants set by \({H}_B\). This latter corollary constitutes a 2nd law for appropriate non-compact AdS event horizons.