Relightable interactive scene reconstruction aims to build an editable 3D model from scans of different object arrangements and render new layouts under novel illumination. Existing methods either bake lighting into appearance or recover material and illumination only for fixed scenes, leaving edited layouts with inconsistent shadows and indirect lighting. We present LightFuse, a 2D Gaussian framework that extends interactive scene reconstruction with explicit material-illumination decomposition and physically based relighting. LightFuse first fuses observations across states to reconstruct a shared background and movable objects. It then conducts ray-tracing-oriented geometry refinement to produce more complete and consistent surfaces. On the refined geometry, staged training with differentiable one-bounce ray tracing separates shared metallic--roughness material from state-specific environment lighting. The resulting scene supports object rearrangement, material editing, and relighting, while ray tracing recomputes appearance after each interaction. Experiments across synthetic scenes demonstrate state-of-the-art relighting quality, outperforming the strongest baseline by +9.74\,dB PSNR and +0.121 SSIM on average. Project page: https://zhn202.github.io/LightFuse/

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