We investigate the microscopic mechanisms of ultralow lattice thermal conductivity (κl) in Tl3VSe4 by combining a first principles density functional theory based framework of anharmonic lattice dynamics with the Peierls-Boltzmann transport equation for phonons. We include contributions of the three- and four-phonon scattering processes to the phonon lifetimes as well as the temperature dependent anharmonic renormalization of phonon energies arising from an unusually strong quartic anharmonicity in Tl3VSe4. In contrast to a recent report by Mukhopadhyay et al. Science 360, 1455 (2018) which suggested that a significant contribution to κl arises from random walks among uncorrelated oscillators, we show that particlelike propagation of phonon excitations can successfully explain the experimentally observed ultralow κl. Our findings are further supported by explicit calculations of the off-diagonal terms of the heat current operator, which are found to be small and indicate that wavelike tunneling of heat carrying vibrations is of minor importance. Our results (i) resolve the discrepancy between the theoretical and experimental κl, (ii) offer new insights into the minimum κl achievable in Tl3VSe4, and (iii) highlight the importance of high order anharmonicity in low-κl systems. The methodology demonstrated here may be used to resolve the discrepancies between the experimentally measured and the theoretically calculated κl in skutterides and perovskites, as well as to understand the glasslike κl in complex crystals with strong anharmonicity, leading towards the goal of rational design of new materials.