Abstract: Based on first-principles calculations, we study the structural stability of the H and T phases of monolayer MoS2 upon Li doping. Our calculations demonstrate that it is possible to stabilize a distorted T phase of MoS2 over the H phase through adsorption of Li atoms on the MoS2 surface. Through molecular dynamics and phonon calculations, we show that the T phase of MoS2 is dynamically unstable and undergoes considerable distortions. The type of distortion depends on the concentration of adsorbed Li atoms and changes from zigzag-like to diamond-like when increasing the Li doping. There exists a substantial energy barrier to transform the stable H phase to the distorted T phases, which is considerably reduced by increasing the concentration of Li atoms. We show that it is necessary that the Li atoms adsorb on both sides of the MoS2 monolayer to reduce the barrier sufficiently. Two processes are examined that allow for such two-sided adsorption, namely, penetration through the MoS2 layer and diffusion over the MoS2 surface. We show that while there is only a small barrier of 0.24 eV for surface diffusion, the amount of energy needed to pass through a pure MoS2 layer is of the order of similar or equal to 2 eV. However, when the MoS2 layer is covered with Li atoms the amount of energy that Li atoms should gain to penetrate the layer is drastically reduced and penetration becomes feasible.