My understanding is that if you use a lead vessel in combination with an acidic liquid such as orange juice, wine, vinegar or milk, some of the lead will dissolve into the liquid and form lead acetate.
From the Wikipedia:
"Lead acetate is a chemical compound, a white crystalline substance with a sweetish taste. It is made by treating lead oxide with acetic acid. Like other lead compounds, it is toxic. Lead acetate is soluble in water and glycerin.
The old Romans were quite fond of a drink called "Sugar of Lead" which is really lead acetate. Lead acetate has a sweet taste, which has led to its use as a sugar substitute throughout history. The ancient Romans, who had few sweeteners besides honey, would boil must (grape juice) in lead pots to produce a reduced sugar syrup called defrutum, concentrated again into sapa. This syrup was used to sweeten wine, and to sweeten and preserve fruit. It is possible that lead acetate or other lead compounds leaching into the syrup might have caused lead poisoning in anyone consuming it."
The Romans were fond of using lead in dinnerware and goblets. After a while, the Patricians or upper class Romans, had fewer children and many children were born with birth defects. Some of their leaders were off the chart nuts.
I don't think that washing lead with neutral PH or basic PH water for a short time will cause any lead to mix with the water.
It is also my understanding that if a lead shot fall area is part of a watershed, it can be treated with lime to limit any transfer of lead into ground water.
Lead is not water soluble. Lead will form some compounds such as lead carbonate and lead acetate (mentioned above) that are water soluble. Formation of most of these water soluble lead compounds is pH dependent.
Lead can become suspended in water by using sulfuric acid to dissolve it. Acid rain can have some affect on lead also which is why some clubs are use lime on their drop zones. Also, the biodegradable birds have an effect also. I think their PH is 3, 7 is neutral.