Oh, right, language barrier! It's funny, because when I put "lunch box" into an image search I get exactly the thing you describe. And maybe that's what younger people in the US picture? For those of us raised in the 70s-80s in the US, a lunch box is a rectangular metal (or sometimes plastic) box with a handle, for carrying lunch. (Do an image search for "1980s lunch box" to get a sense of it.) It's not a thing you'd put into a picnic basket...but the thing you describe totally is.
Well, and now we both know! :-)