Materials with low lattice thermal conductivity κ_L have great potential in thermoelectrics, heat management, and other frontier fields. Combining Boltzmann transport theory with the Allen–Feldman model, we predict a low κ_L of 0.5 W m⁻¹ K⁻¹ at 850 K in BaSnS₂, later confirmed by experimental results. We show that the off-diagonal part of κ_L contributed by wave-like tunneling phonons becomes pronounced at high temperatures and leads to a deviation of the temperature dependence of κ_L from T^-1 to T^-0.76, implying the lattice anharmonicity in BaSnS₂. Further analyses indicate over 68% of κ_L is contributed by optical phonons, owing to their relatively high group velocity. These optical modes are visualized as anti-phase vibrations in BaSnS₂ monolayers originating from the unique permutation of SnS₃ tetrahedra. By investigating the mode-resolved group velocity, relaxation time, and Grüneisen parameter, we attribute the intrinsic low κ_L to the soft lattice and the high lattice anharmonicity induced by the Ba–S weak bonding and Sn(II) lone pair electrons. Our study uncovers the microscopic mechanism of optical-phonon-dominated heat transport in BaSnS₂ and suggests it worthy of further experimental studies as an intrinsic-low-κ_L material.