The geopolymer -- an inorganic polymeric material synthesized from the reaction of aluminosilicate precursors and alkaline activating solutions -- has gained wide research attention in recent decades as a promising adsorbent for the removal of aqueous heavy metals. However, the high variability of the material and several unanswered questions have limited its development and general adoption in the industry. This study evaluates the impacts of composition and microstructure on the performance of geopolymers for aqueous lead (Pb) removal to elucidate the composition-structure-property relationship. The Pb sorption kinetics and efficiency of four geopolymers, prepared using different fly ash precursors and activating solutions, were investigated. Although all the four geopolymer compositions studied displayed a high Pb removal efficiency of over 99.5%, with a slight decrease in efficiency with increasing Ca/(Si + Al) and Al/Si contents, the results show that the sorption kinetics decreases exponentially with increasing Ca/(Si + Al) and Al/Si molar ratios. The performance of the geopolymers also shows strong correlation to the microstructure, wherein the sorption kinetics increases exponentially, while the efficiency increases slightly, with increasing mass fraction of the amorphous phase in the geopolymer's phase assemblage. The results of this research indicate that using appropriate precursor formulation and curing conditions to evoke the best microstructures, geopolymer materials can be optimized for high performance in removing heavy metals, thereby improving the chances of the material's general acceptability in the adsorbent industry.