To address the safety problems of lithium-ion batteries mainly caused by to flammable liquid electrolytes, all-solid-state-lithium-batteries (ASSLBs) with solid-state electrolytes are considered as potential replacement candidates. For ASSLBs, inorganic solid-state electrolytes are preferred mainly due to their wide temperature operation windows, better Li mobility and safety. Among the popular solid-state electrolytes, Li7La3Zr2O12 (LLZO) with a garnet structure has been shown to have favorable properties. Understanding the transport properties of Li atoms in LLZO is very crucial because the diffusion mechanism of Li atoms dictates the ionic conductivity among other factors. The main goal of this Muon study is to quantify the Li diffusion rates in LLZO and its interface with cathode with respect to the Grain boundary concentration and morphology.