Solid electrolytes for solid-state Li-ion batteries are stimulating considerable interest for next-generation energy storage applications. The Li$_7$La$_3$Zr$_2$O$_{12}$ garnet-type solid electrolyte has received appreciable attention as a result of its high ionic conductivity. However, several challenges for the successful application of solid-state devices based on Li$_7$La$_3$Zr$_2$O$_{12}$ remain, such as dendrite formation and maintaining physical contact at interfaces over many Li intercalation/extraction cycles. Here, we apply first-principles density functional theory to provide insights into the Li$_7$La$_3$Zr$_2$O$_{12}$ particle morphology under various physical and chemical conditions. Our findings indicate Li segregation at the surfaces, suggesting Li-rich grain boundaries at typical synthesis and sintering conditions. On the basis of our results, we propose practical strategies to curb Li segregation at the Li$_7$La$_3$Zr$_2$O$_{12}$ interfaces. This approach can be extended to other Li-ion conductors for the design of practical energy storage devices.