Lunch pail is not a modern term but I heard it growing up in the 60's. My own father carried a lunch pail - small circular metal container that was stacked (at least two components) and had a metal cover and a handle like a pail. We referred to it in pidgin as "kaukau tin".
I looked up the origin in Pukui dictionary. The kini in this case is a transliteration of the English word tin...from plantation days when workers brought lunches in tin pails. She also calls it 'kini 'ai, which makes sense. Where did 'o' come from?