Extensive research interest on lunar construction materials, represented by lunar geopolymers, has been driven by the worldwide programs of in-situ lunar exploration. This study comprehensively investigates different combinations between diverse lunar regolith simulants and activators at various curing temperatures, and their effects are revealed by the mechanical properties, microstructure, and composition of resulting lunar geopolymers. This study proposes that glass-rich lunar regolith should be activated by sodium hydroxide to ensure the aluminosilicate dissolution and form dense zeolitic products, whereas sodium silicate is more suitable for glass-free lunar regolith to assist the generation of amorphous products. Additionally, the temperature for the thermal curing of lunar geopolymers should exceed 60-80 degrees C for applicable 24-hour strength. Based on experimental characterizations and statistical analysis of existing data, three determinants of lunar geopolymer synthesis can be emphasized including the compatibility between activator and regolith activity, the calcium and alkali content of regolith, and the temperature of sealed thermal curing. These principles provide valuable guidance on the selection of regolith and activators along with the establishment of curing protocols towards future lunar constructions.