Understanding the microscopic origin of intrinsically low lattice thermal conductivity is crucial for the design of thermoelectric materials. Here, the lattice dynamics and thermal transport of layered $X\mathrm{Ag}Y (X=\mathrm{K},\mathrm{Rb},\mathrm{Cs};Y=\mathrm{S},\mathrm{Se},\mathrm{Te})$ compounds with the P4/nmm structure are investigated using first-principles calculations by explicitly accounting for high-order anharmonicity and phonon coherence. All $X\mathrm{Ag}Y$ compounds exhibit remarkably low lattice thermal conductivity, with ${\kappa }_L$ at 300 K confined to a narrow range of approximately 0.334–$0.643\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, reaching as low as $0.334\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ in CsAgTe. The strong suppression of the incoherent (Peierls-type) contribution originates from pronounced quartic anharmonicity and enhanced four-phonon Umklapp scattering, which can be traced to the distorted Ag–Y tetrahedral environment and the associated nonuniform distribution of bonding rigidity, giving rise to an anomalously strong bond–strong anharmonicity coupling. Beyond the phonon gas model, coherent phonon transport becomes non-negligible at elevated temperatures, particularly along the $c$ axis, arising from strong inter-branch coupling among high-frequency optical phonons that enables wave-assisted energy transfer. These results reveal a cooperative mechanism combining high-order anharmonicity and phonon coherence, providing a transport paradigm beyond the Peierls picture for intrinsically low-${\kappa }_L$ layered materials.

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• Lattice dynamics
• Phonons
• Thermal conductivity
• Thermal transport
• Thermoelectric effects
• Thermoelectric transport
• Thermoelectrics