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Hydrogen emission lines can provide extensive information about star-forming galaxies in both the local and high-redshift Universe. We present a detailed Lyman continuum (LyC), Lyman-α (Lyα), and Balmer line (Hα and Hβ) radiative transfer study of a high-resolution isolated Milky Way simulation using the state-of-the-art Arepo-RT radiation hydrodynamics code with the SMUGGLE galaxy formation model. The realistic framework includes stellar feedback, non-equilibrium thermochemistry accounting for molecular hydrogen, and dust grain evolution in the interstellar medium (ISM). We extend our publicly available Cosmic Lyα Transfer (COLT) code with photoionization equilibrium Monte Carlo radiative transfer and various methodology improvements for self-consistent end-to-end (non-)resonant line predictions. Accurate LyC reprocessing to recombination emission requires modelling pre-absorption by dust ($f_\text{abs} \approx 27.5\,\rm{per\,\,cent}$), helium ionization ($f_\text{He} \approx 8.7\,\rm{per\,\,cent}$), and anisotropic escape fractions ($f_\text{esc} \approx 7.9\,\rm{per\,\,cent}$), as these reduce the available budget for hydrogen line emission ($f_\text{H} \approx 55.9\,\rm{per\,\,cent}$). We investigate the role of the multiphase dusty ISM, disc geometry, gas kinematics, and star formation activity in governing the physics of emission and escape, focusing on the time variability, gas-phase structure, and spatial spectral, and viewing angle dependence of the emergent photons. Isolated disc simulations are well-suited for comprehensive observational comparisons with local Hα surveys, butmore »would require a proper cosmological circumgalactic medium (CGM) environment as well as less dust absorption and rotational broadening to serve as analogs for high-redshift Lyα emitting galaxies. Future applications of our framework to next-generation cosmological simulations of galaxy formation including radiation-hydrodynamics that resolve ≲10 pc multiphase ISM and ≲1 kpc CGM structures will provide crucial insights and predictions for current and upcoming Lyα observations.