Two-dimensional (2D) InSe, which exhibits high electron mobility and a wide band gap has emerged as a promising material for photoelectric and thermoelectric applications. The inadequate understanding of the lattice thermal conductivity (κ), however, hampers the advancement of 2D InSe. Herein, by taking into account anharmonicity up to the fourth order and introducing the equibiaxial tensile strain (ϵ), we have performed an in-depth study on the lattice dynamics of 2D InSe. Interestingly, the κ exhibits a non-monotonic behaviour as a function of equibiaxial tensile strain, which can be attributed to the changes in acoustic phonon lifetimes. At the Γ point, a blue-shift of the lowest optical mode and a red-shift of the uppermost optical mode are reported for the first time. More strikingly, the blue-shift can be largely suppressed by equibiaxial tensile strain. Further study indicates that the unique transition of the potential energy surface is responsible for the disappearance of the blue-shift. Our work may enlighten the future research on phonon engineering and management of the lattice thermal conductivity of 2D InSe.