because Italians who used it in English just didn't know the English term for it and placed two words of their native language into the foreign and kept it there instead of using the proper expression

Oh, but there is. The word is "lingua franca," which has an entry in the American Heritage Dictionary, Merriam-Webster, and the OED. I just checked. "Lingua franca" is just as much an English word as "menu," "aileron," "alcohol," "taiga," "tundra," "lasso," "canyon," "daiquiri," "alumnus," "dilemma," or "flotilla."