Per se there is no legal need for an ID for a domestic flight nor for a Schengen flight in Europe. When crossing a border your ID might be checked by border police as well as in countries requiring to carry a valid ID with you.

Some countries require IDs for air travel, some companies do so as well. Some have a really efficient process and do not require anything (Spoiler: not Portugal).

Take your passport with you.

Driver licenses are not valid IDs in Europe, only passports and EEC national ID cards are.

Staff at Lisbon airport is pretty untrained and does not recognize many valid EU national IDs asking for passports.