The development of analytical methods for the determination of metal ions in water is one of the priority tasks for efficient environmental monitoring. The use of modified gold nanoparticles and the colorimetric detection of their aggregation initiated by ions binding with specific receptors on the nanoparticle surface has high potential for simple testing. However, the limits of this approach and the parameters determining the assay sensitivity are not clear, and the possibilities of different assay formats are estimated only empirically. We have proposed a mathematical description of the aggregation processes in the assay and have estimated the detection limits of an aptamer-based assay of Pb²⁺ ions theoretically and experimentally. In the studied assay, gold nanoparticles modified with G,T-enriched aptamer were used, and their aggregation caused by the interaction with Pb²⁺ ions was controlled via a color change. The experimentally determined limit of Pb²⁺ detection was 700 ppb, which was in good agreement with theoretical calculations. An examination of the model showed that the limiting parameter of the assay is the binding constant of the aptamer–Pb²⁺ ion interaction. To overcome this limitation without searching for alternate receptors, two methods have been proposed, namely additional aggregation-causing components or centrifugation. These approaches lowered the detection limit to 150 ppb and even to 0.4 ppb. The second value accords with regulatory demands for the permissible levels of water source contamination, and the corresponding approach has significant competitive potential due to its rapidity, simple implementation, and the visual assessment of the assay results.