When something which is generally accepted as being common law passes into legislation it is referred to as a tort law. This can then be sued against.

The immediate pursuit would be against the manufacturer of the object. Secondarily, the manufacturer of the paint could be pursued if the original pursuit was not succesful.

In this circumstance, depending on the prevailing jurisdictional environment and statutes at the time, it might well be possible to pursue legislation either against the manufacturer of the object or potentially the supplier of the paint.

If you were legally representing the child, you would look to prove that the manufacturer of the object was negligent or knowledgably used lead in the manufacturing process. If you were the manufacturer, you would look to prove that the material supplied to you be the supplier conformed to all legal requirements at that time and that therefore you were not legally at fault. The supplier would argue that knowledge around lead poisoning was an unknown development at that time.

To find out more about tort law I would go to the law society.