Magnesium–lithium alloys are arguably the lightest metal structural materials but have low strength. In order to increase strength, friction stir processing (FSP) is applied to a hot-rolled Mg-10Li-3Al-3Zn (LA103Z) sheet to study the effects on the microstructure and mechanical properties. In this study, the strengthening mechanisms of various FSP regions of an Mg-Li alloy were clarified by a combination of numerical simulation and experimental method. Based on ANSYS APDL, a finite element model with a moving heat source is established. Rotational speeds of 800, 1000, and 1200 rpm and traverse speeds of 100, 110, and 120 mm/min were used in this research. The simulation results confirm that the influence of the rotation speed on the alloy temperature field is greater than that of the travel speed. The temperature of the processing area increases with an increase in rotation speed and decreases with an increase in travel speed. Then, hot-rolled LA103Z alloy plates are processed by FSP. The correspondence between the numerical simulation and experiment was verified by infrared thermography. The results indicate that FSP decreases the grain size significantly for the dynamic recrystallization and dramatic mechanical crushing of the stirring pin. The α-Mg and AlLi are solid soluted in the β-Li matrix. The tensile strength of the processing zone is 260.67 MPa (1000 rpm, 110 mm/min) versus the 170.47 MPa of the base metal. The SZ has the highest microhardness of 77.8 HV (800 rpm, 120 mm/min) and decreases gradually to the BM. The severe deformation, recrystallization, and solid solution of the α-Mg are important factors contributing to the improved mechanical properties.