Eu2+-activated alkali-lithosilicate phosphors exhibit narrow-band emissions that are attractive to high color-rendition and wide color-gamut displays. The microscopic mechanism behind the small emission bandwidth is not presently understood. Here, we report an explicit calculation of the vibronic process occurring in the narrow-band green emission of Rb2Na2[Li3SiO4]4:Eu2+. We show that due to the high rigidity of the host material, the structural strain induced by the localized Eu2+ 4f-5d excitation is distributed among the atoms far beyond the first coordination shell and hence reduces the local structural relaxation around Eu2+. The emission bandshape is thus mainly controlled by the coupling of the electronic transition with the phonon modes associated with motions of host constituent atoms, which was further validated by the good agreement of the calculated bandshape with the experiment. The results provide insights into the generation of narrow-band emission and improve our knowledge on electron-phonon coupling of 4f-5d transitions in phosphors.