I doubt if the Romans used lead just for sweetening their food.
They used lead pipes for conduct water from aqueducts to their homes and (this was more dangerous) used lead for making food vessels and wine cups. Wine, that contains organic acids, can dissolve some lead.
4CH3COOH + 2Pb + O2 = 2(CH3COO)2Pb + 2H2O
Organic salts of lead (especially acetate) are very sweet so this improved taste of wine (rather tasteless at that times). And that weekness for wine drinked of lead cups may be the main reason of lead poisoning.
At our times some people drink tasteless coffee and try to improve their taste by smoking.