Lithium-intercalated layered transition-metal oxides, LixTMO2, brought about a paradigm change in rechargeable batteries in recent decades and show promise for use in memristors, a type of device for future neural computing and on-chip storage. Thermal transport properties, although being a crucial element in limiting the charging/discharging rate, package density, energy efficiency, and safety of batteries as well as the controllability and energy consumption of memristors, are poorly managed or even understood yet. Here, for the first time, we employ quantum calculations including high-order lattice anharmonicity and find that the thermal conductivity k of LixTMO2 materials is significantly lower than hitherto believed. More specifically, the theoretical upper limit of k of LiCoO2 is 6 W/m-K, 2-6 times lower than the prior theoretical predictions. Delithiation further reduces k by 40-70% for LiCoO2 and LiNbO2. Grain boundaries, strains, and porosity are yet additional causes of thermal-conductivity reduction, while Li-ion diffusion and electrical transport are found to have only a minor effect on phonon thermal transport. The results elucidate several long-standing issues regarding the thermal transport in lithium-intercalated materials and provide guidance toward designing high-energy-density batteries and controllable memristors.