Antiperovskites have attracted significant interest in the field of energy conversion in recent years. While extensive research has focused on the magnetism, ionic conductivity and superconductivity of antiperovskites, their thermal properties including lattice anharmonicity and thermal transport remain less explored compared to their well-studied perovskite counterparts. Recently, nitrohalide double antiperovskites have been successfully synthesized. In this work, we investigate the thermal transport properties of nitrohalide double antiperovskites Li₆NII₂ and Li₆NBrBr₂ using first-principles machine-learning potentials. Our results reveal that within the perturbation theory framework, imaginary phonons appear throughout the entire Brillouin zone in both the harmonic regime and at elevated temperatures. Atomic vibrational analysis indicates that stochastic Li-ion movements confined within a single conventional unit cell are responsible for the presence of these imaginary phonons. Furthermore, homogeneous nonequilibrium molecular dynamics and equilibrium molecular dynamics simulations demonstrate that Li₆NII₂ and Li₆NBrBr₂ exhibit ultralow glass-like lattice thermal conductivities. Spectral thermal conductivity analysis shows that the dominant contributions arise from phonons with frequencies below 5 THz and around 11 THz. The substantial phonon contribution near 11 THz is attributed to the confined stochastic motions of Li ions. This work uncovers the unconventional microscopic cation dynamics and strong lattice anharmonicity in double antiperovskites Li₆NII₂ and Li₆NBrBr₂, thereby advancing the understanding of phonon transport in these materials.