For the question of lead pipes, the 2014 paper Lead in ancient Rome’s city waters, by Hugo Delile et al, probably contains emore that enough detail to answer the question. The authors concluded that:
Lead pollution of “tap water” in Roman times is clearly measurable, but unlikely to have been truly harmful
But piped water was by no means the only source of lead in the ancient Roman diet. In 1983, the Canadian geologist Jerome O. Nriagu put forward a theory that dietary lead was a major contributing factor in the fall of Ancient Rome (in the book Lead and Lead Poisoning in Antiquity and the paper Saturnine Gout among Roman Aristocrats — Did Lead Poisoning Contribute to the Fall of the Empire?).
To give one example, it was common in Ancinet Rome to sweeten wine with a syrup made from boiled grapes. The grapes were boiled in vessels made from, or lined with lead. Experimental archaeologists replicated the process and tested the results. They found that the syrups contained between 240 and 1000 milligrams of lead per litre.
As Nriagu observed,
"One teaspoon (5ml) of such syrup would have been more than enough to cause chronic lead poisoning,"
However, the effects on Rome's ruling elite that Nriagu hypothesised might have been caused by chronic lead poisoning (like the symptoms exhibited by Claudius, for example) may be the result of a number of different causes. As Nriagu himself observed, the causes of the maladies with which Claudius was afflicted are:
"... a matter of longstanding debate."
Nriagu's conclusions were challenged almost immediately, notably by John Scarborough in his 1984 review of Nriagu's work titled The Myth of Lead Poisoning among the Romans: An Essay Review.
Further, since 1983 a number of skeletal remains from the Imperial Roman period have been tested for evidence of lead poisoning. Although there are some examples that exhibit evidence of lead poisoning (or even severe lead poisoning, as Kristina Killgrove observed in the article Lead Poisoning in Rome - The Skeletal Evidence), this is by no means common.