Lithium lanthanum titanate perovskites (LLTO) are excellent solid electrolytes because of their good ionic conductivity and elasticity. Here, the effects of high hydrostatic pressure and the impact of the position of Li impurities on the structural, electronic, elastic, and Li-ion diffusion properties of LaTiO3 perovskite (LTO) and its LLTO substitutional solid solutions, were studied. Density-functional theory (DFT) and Hubbard-corrected local density approximation (LDA+U) were used. Due to hydrostatic pressure, the octahedral distortion of LTO, LLTO-layered (L), and -rock-salt (RS) electrolytes decreases, while it increases for the LLTO-columnar (C). On the other hand, the energy band gap (Eg) of LTO and LLTO-C decrease as hydrostatic pressure increases. For the LLTO-L, Eg increases with pressure. For the LLTO-RS, Eg decreases from zero to 20 GPa and increases from 20 to 30 GPa. Pugh’s criterion indicates that all systems are ductile regardless of applied pressure. Poisson’s ratio shows that bonds in the LTO are metallic, and LLTO-C is ionic-covalent. Likewise, LLTO-L and -RS electrolytes have a transition from ionic-covalent to metallic behavior, as pressure increases. Li-ion diffusion barriers of LLTO electrolytes increase with increasing hydrostatic pressure, indicating a decrease in Li ionic conductivity.