Solubility of Lead in water from leaded pipes in Roman aqueducts
Let me give an extreme example of chemical analysis. It is an anecdote. Some analytical chemists were using a very sensitive technique to analyze metals in blood. It is called neutron activation analysis. What they saw was that a very small quantity of molybdenum (Mo) was present in small quantities persistently. Nobody expected that. It turned out after a lot of hard work that Mo was coming from the stainless steel syringe needle used for drawing blood. Lesson of the story: There is nothing which is perfectly insoluble in water. It all depends on the analytical technique. If you try to weigh a hair on a "weighing machine" it will tell you that the mass is zero kg, but if you use a fine analytical balance it will tell you that hair has a mass.

The same goes for lead pipes. Natural water has plenty of minerals, dissolved oxygen anions, cations and don't forget the microorganisms. The bacteria do a lot of chemical transformations in water. As a result, Pb would slowly leach into the water at parts per million or parts per billion levels. Don't assume that Romans were drinking lead salt solutions in high concentration ranges. Not only water lead was present in water, it was also present in alcoholic beverages.

Read more here Lead in ancient Rome’s city waters

Lead in water is still a serious problem in several areas of the modern world. It is not an ancient problem.