Superionic crystals reach an ionic conductivity comparable to liquid electrolytes following a superionic transition at high temperature. The physical mechanisms that lead to this behaviour remain poorly understood. It has been proposed that superionic transitions are accompanied by the breakdown of specific phonon modes linked to characteristic diffusion processes. Any changes in vibrational properties across the superionic transition may therefore provide insights into the underlying physics of this phenomenon. Here, we apply a combination of lattice dynamics and ab initio molecular dynamics to probe the vibrational properties of the archetypal superionic conductor Li3N. We assess harmonic, quasi-harmonic, and anharmonic descriptions of the phonons. The harmonic and quasi-harmonic models show no change in features across the superionic transition. The fully anharmonic model, however, exhibits a phonon breakdown for all modes above the superionic transition temperature. The implications for developing lattice-dynamics based descriptors for superionic conductors are discussed.