The Lumina project marks a methodological leap in cosmological modeling by running radiation-hydrodynamics across a 500 comoving megaparsec box with 2×6000³ resolution elements, self-consistently tracking HI, HeI, and HeII reionization to z=3 using AREPO plus a six-bin M1 solver on top of the IllustrisTNG galaxy formation model. This preprint (arXiv:2605.15310) yields a stellar-driven hydrogen reionization completing around z≈5.2 with lingering neutral patches to z≈4.75, followed by AGN-driven HeII reionization finishing near z=3, while reproducing Planck's Thomson optical depth. Unlike prior smaller-volume efforts such as Thesan, which captured local topology but suffered from cosmic variance in rare AGN environments, Lumina's scale directly links feedback prescriptions to large-scale IGM topology, revealing a clear thermal boost during HeII reionization that aligns with Lyman-alpha forest temperature measurements. Original coverage underplays how including baryon-dark matter streaming velocities alters early galaxy formation efficiency, an effect that propagates into reionization patchiness and could reconcile tensions with JWST's abundant bright galaxies at z>10. By extending the calibrated TNG framework (Pillepich et al. 2018) into radiation transport, Lumina enables forward-modeling of 21-cm signals and metal absorbers that smaller boxes distort, though it inherits TNG's subgrid feedback assumptions and uses only six frequency bins, limiting spectral precision. These choices trade some microphysical detail for statistical power over rare objects and environments.