Perovskite-structured lithium lanthanum titanate (LLT, La2/3-xLi3xTiO3, 0< x<0.16) is a promising solid electrolyte with high lithium ion conductivity and a good model system to understand lithium ion diffusion behaviors in solids. Molecular dynamics (MD) and related atomistic computer simulations were used to study the diffusion behavior and diffusion mechanism as a function of composition in LLT solid-state electrolytes. The effect of defect concentration on the structure and lithium ion diffusion behaviors in LLT was systematically studied using MD simulations and molecular static calculations with the goal to obtain fundamental understanding of the diffusion mechanism of lithium ions in these materials. The simulation results show that there exists an optimal vacancy concentration at around x=0.067 at which lithium ions have the highest diffusion coefficient and the lowest diffusion energy barrier. The lowest energy barrier from dynamics simulations was found to be around 0.22eV, which compared favorably with 0.19eV from static nudged elastic band calculations. It was also found that lithium ions diffuse through bottleneck structures made of oxygen ions, which expand in dimension by 8%-10% when lithium ions pass through. By designing perovskite structures with larger bottleneck sizes can be a means of further improving lithium ion conductivities in these materials.