This work derives the full framework of General Relativity from the Sobolev–Ozok Lattice (SOL) model, a discrete spacetime structure in which curvature emerges from the coherence tension of Planck-scale cells. Starting from the SOL action, the Einstein field equations are obtained without assuming the continuum theory a priori. The derivation naturally incorporates the Newtonian limit and post-Newtonian corrections, linking the lattice microphysics directly to classical gravitational dynamics. This approach shows how the familiar geometric description of gravity arises from a deeper discrete foundation, offering new insights into the relationship between spacetime microstructure and macroscopic gravitational phenomena. Decleration of Tools Used: This paper was prepared and formatted using Overleaf (LaTeX editor). Text refinement and language polishing were assisted by Overleaf AI Editor. all scientifit content, derivations, and conclusions are original and autored by the undersigned. This paper is part of the Sobolev–Ozok Lattice (SOL) research program. Project webpage (papers, figures, updates): https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/