I said that the song was lost, not that the tune was lost.

Yes "Greensleves" is a discant on the romanesca, or cut time passamezzo antico, and sometimes both. John Ward noted (JAMS XX, 1967)) that as a result "Greensleeves" was a type rather than a specific tune. Note that there are 6 versions of it in the broadside ballad tune ABC files on my website.