All I can think of is "lunchbox" (even if it's for a different meal, it's still called that--US).

The image that comes to mind when you say "lunchbox" here is a painted rectangular box with a snap-closable hinged lid, about 20 x 30 x 10cm (guessing the size--I don't have a model in front of me). It often has a place inside where a small Thermos bottle (vacuum flask) can be fastened. That doesn't sound too different from your example.

If it were open and made of cane, we might call it a picnic basket, but then it's usually for carrying food for many, and a "lunchbox" is only for one person.

I saw one of these in an Asian supermarket the other day and it was simply called "food carrier". I think a lunch box is something quite different, because you can't transport soup or "Eintopf" or rice pudding (!) in it. By the way I know it in German as "Mitchen", an expression I love.

A lunchbox won't work for liquid stuff (if you don't want it to leak all over the place). I saw food carrier, too. They are nowadays made of plastic or aluminium. I also saw foodtainer or food-tainer, but I think this is the name of a special product series of that kind.

Get that damn thermos away from me!

You can put liquidy foods or drinks in a thermos, which is insulated so it keeps things warm (or cold). You probably wouldn't put Butterbrot in one though. Usually you'd see a worker taking a thermos and a lunchbox.

Check out the URL for a picture I found of things called "Henkelmann". I can only say, "sowas gibt's bei uns (Amerikaner) nicht." The best description I could give would be "insulated food container"...