Garnet structured cubic LLZO crystal (Li56La24Zr16O96) is one of the most promising solid electrolytes for next-generation solid-state lithium-ion batteries. Ab initio molecular dynamics simulations have been employed to study the impacts of lithium vacancy defect and doping concentration on the lithium ionic conductivity and stability of LLZO. The number of lithium atoms in a unit cell of LLZO has been reduced from 56 to 53, where 56 lithium atoms represent the structure of stoichiometric LLZO, i.e., Li7La3Zr2O12. Similarly, the effect of Al and Ga doping on the conductivity and stability of LLZO material was also investigated. Our computational results confirm that both the defects help in enhancing the conductivity of LLZO and the concentration of defect introduced controls the trade-off between the conductivity and stability. Overall, this study provides a valuable insight into the enhancement of conductivity of cubic LLZO garnet material along with structural stability.