We investigate the effect of non-analytical corrections on the phonon thermal transport properties in two-dimensional indium chalcogenide compounds. The longitudinal optical (LO) and transverse optical (TO) branches in the phonon dispersion are split near the Γ-point. The lattice thermal conductivity of monolayer InS is increased by 30.2% under non-analytical corrections because of the large LO-TO splitting at Γ-point. The predicted lattice thermal conductivities with non-analytical corrections at room temperature are 57.1 W/mK, 44.4 W/mK and 33.1 W/mK for the monolayer InS, InSe and InTe, respectively. The lattice thermal conductivity can be effectively reduced by nanostructures because the representative mean free paths are found very large in these monolayers. By quantifying the relative contribution of the phonon modes to the lattice thermal conductivity, we predict that the longitudinal acoustic branch is the main contributor to the lattice thermal conductivity. Due to the low lattice thermalconductivities of these monolayers, they can be useful in the nanoscale thermoelectric devices.