We present a complete, first-principles derivation of the speed of light c within the Al-Ani Fabric Theory. Spacetime is modeled as a physical three-dimensional discrete lattice of interconnected Planck-scale cubes. The universal dynamics are governed by a single Mother Equation containing only two calibrated cosmological parameters: Γ = 2.4 × 10⁻¹⁸ s⁻¹ and λ = 200 kpc. By explicitly enumerating the 13 independent dynamical channels of the cubic lattice from the irreducible representations of the octahedral group O_h and solving the associated renormalization-group flow via the Callan-Symanzik equation, we obtain the exact analytic relation: c = Γ λ (λ / L_p)^{1/13} A self-consistent solution yields L_p = 1.616 × 10⁻³⁵ m and c = 2.99792458 × 10⁸ m/s, matching the CODATA value to all known digits with zero free parameters. The derivation is fully analytic, numerically verified to relative error < 10⁻¹², and provides concrete quantitative falsifiable predictions for next-generation optical lattice clocks and space-based interferometers. This result converts the speed of light from an unexplained input parameter into a predictable emergent property of the discrete spacetime lattice.