The recently discovered Sr[Li2Al2O2N2]:Eu2+ red phosphor, candidate for the next generation of eco-efficient white light-emitting diodes, exhibits excellent emission spectral position and exceptionally small linewidth. It belongs to the UCr4C4-structure family of phosphors containing many potential candidates for commercial phosphors, whose small linewidth, tentatively ascribed to the high-symmetry cuboid environment of the doping site, has drawn the attention of researchers in the last five years. Density functional theory, Delta SCF method, and configuration coordinate models (CCM) are used to provide a complete characterization of this material. Using a multi-dimensional CCM, an accurate description of the coupling of the vibronic structure with the electronic 5d -> 4f transition is obtained, including the partial Huang-Rhys factors and frequency of the dominant modes. It is shown that, in addition to the first-coordination shell cuboid deformation mode, low-frequency phonon modes involving chains of strontium atoms along the tetragonal axis shape the emission linewidth in Sr[Li2Al2O2N2]:Eu2+. This finding sheds new light on the emission properties of UCr4C4-structure phosphors, possessing similar Ca/Sr/Ba channel. The approach provides a robust theoretical framework to systematically study the emission spectra of such Eu-doped phosphors, and predict candidates with expected similar or even sharper linewidth.