This has been alleged, but as far as I know, not proven. AFAIK no ancient Roman text says anything about using lead acetate (or something whose production was described and could plausibly be taken as “sugar of lead”) as a sweetener. The closest anything says is that Romans prepare sweeteners by boiling down fruit juices and squeezings, sometimes in lead pots. You could argue that the fruit acid acting on the lead produced lead acetate, but the fruits themselves contained the sugars they were truing to render down.
(Pliny apparently preferred the use of lead vessels, but copper ones were used as well)
In any event, they certainly were getting lead from their plumbing.
I was being facetious, but the levels of lead in Roman domestic plumbed water has been shown to be two orders of magnitude above the source spring water. Not acute lead poisoning, but not nothing, either.
The issue with lead acetate I have heard was the storing of wine in lead lined containers. Oxidised alcohol is acetic acid (aka vinegar) and will attack the lead to form lead acetate. So sour spoiled wine will rejuvenate into a sweet wine of clear toxicity.
Ordinary lead pipes present very little danger. Even in relatively recent time potable water came through lead pipes. Lead does after all give us the name of the trade of plumber.
It depends on the pH of the water flowing through the pipes, though. You need the right pH, and the right minerals, to form a “scale” over the surface of the lead, which keeps the lead from interacting with the water.
Too low a pH will dissolve the scale, as the residents of Flint, Michigan found out the hard way.