It's actually a bit more complicated. :) They made vessels from copper when they could - copper is a superb heat conductor. But copper gets toxic fast when you cook acidic food. It gets worse if you don't clean your copper vessels. Wikipedia tells:
Copper is reactive with acidic foods which can result in corrosion, the byproducts of which can foment copper toxicity. In certain circumstances, however, unlined copper is recommended and safe, for instance in the preparation of meringue, where copper ions prompt proteins to denature (unfold) and enable stronger protein bonds across the sulfur contained in egg whites. Unlined copper is also used in the making of preserves, jams and jellies.
Despite not having adequate chemistry or medicine, people in old times had a clue - they saw that copper sometimes fouled and turned green, and suspected this was not good, preferring tin-lined copper vessels as the economical alternative to silver-lined copper vessels.
(Needless to say, industries of that time didn't produce stainless steel - maybe some alchemist blacksmith knew enough to make it, but it was not a thing.)
Lining copper pots and pans prevents copper from contact with acidic foods. The most popular lining types are tin, stainless steel, nickel and silver.
...but the chemistry of the time being what it was - shoddy - sometimes tin was contaminated with lead (Pb), sometimes it was deliberately adulterated with lead, and shit happened.
In the middle ages, guilds had a system of proof marks and inspectors to ensure craftsmen wouldn't add too much lead to tin alloys. The Nuremberg standard for example specified 1 part of lead against 10 parts of tin, but in Luzern, Switzerland, a problematic alloy was used.
As for Romans...
However, the use of leaden cookware, though popular, was not the general standard of use. Copper cookware was used far more generally and no indication exists as to how often sapa was added or in what quantity. (Grape syrup)