This research enhances our previously established unified lattice Boltzmann (LB) framework, initially developed for classical Fourier heat conduction and radiation coupling, to now adeptly handle non-Fourier heat conduction and thermal radiation transfer at the micro and nanoscale. It effectively manages the disparities in propagation speeds and complex transient boundary conditions. Validation against one-dimensional benchmarks confirms its accuracy and reliability. The study also examines the influence of critical parameters like the radiative heat transfer parameter Nc, scattering albedo, and optical thickness on thermal dynamics. Significantly, it provides a quantitative error analysis of the steady-state radiation assumption in coupled problems, revealing its limitations under various conditions. This enhanced framework represents a solid improvement in micro and nanoscale multiphysics simulations using the lattice Boltzmann method, ensuring a balance between computational precision and efficiency. It contributes to the development of more refined thermal management strategies in diverse industrial and scientific applications.