We study the role of nonperturbative phonon scattering in strongly anharmonic materials having ultralow lattice thermal conductivity with unusual temperature dependence. We take Tl3VSe4 as an example and investigate its lattice dynamics using perturbation theory (PT) up to the fourth order and molecular dynamics (MD) with a machine-learning potential. We find distinct differences of phonon linewidth between PT and MD in the whole Brillouin zone. The comparison between the theoretical phonon linewidths and experiments suggests that PT severely underestimates the phonon scatterings, even when the fourth-order anharmonicity is included. Moreover, we extend our calculations to higher temperatures and evaluate the two-channel thermal conductivity based on the unified theory developed by Simoncelli et al. [Nat. Phys. 15, 809 (2019)1745-247310.1038/s41567-019-0520-x]. We find a crucial coherence contribution to the total thermal conductivity at high temperatures. Our results pave the path for future studies of phonon properties and lattice thermal conductivities of strongly anharmonic crystals beyond the conventional PT realm.