Based on first-principles calculations in combination with the Boltzmann transport theory, we investigate the effects of onsite Coulomb interaction and strain on the lattice thermal conductivity of the KAgSe monolayer, a recently discovered 2D thermoelectric system with a low lattice thermal conductivity when the onsite Coulomb interaction was not considered (X. Zhang, C. Liu, Y. Tao, Y. Li, Y. Guo, Y. Chen, X. C. Zeng and J. Wang, Adv. Funct. Mater., 2020, 30, 2001200). Our calculations reveal that the onsite Coulomb interaction leads to an increase in the lattice thermal conductivity from 1.22 to 1.82 W m-1 K-1 at room temperature due to the increased phonon group velocity and relaxation time. However, with onsite Coulomb interaction, small 3% biaxial tensile strain can give rise to a 75% considerable decrease in the lattice thermal conductivity at room temperature, from 1.82 to 0.45 W m-1 K-1, which is also much lower than the lattice thermal conductivity of 1.22 W m-1 K-1 without onsite Coulomb interaction and strain. The strain induced decrease of phonon group velocity and enhancement of lattice anharmonicity (large Grüneisen parameter and phase space volume) are responsible for the reduced lattice thermal conductivity. The present work highlights that the onsite Coulomb interaction is indispensable when determining the lattice thermal conductivity of 2D KAgSe, and small tensile strain can greatly decrease the lattice thermal conductivity.