Just in your seats, or private sleeping car accomodation of you go first-class. You might or might not be run out of the lounge car for bringing in your own food, but it is intended for consumption of food purchased on the train. Now, if you just brought the Pop-Tarts, for instance, to go with the 'entree' & beverages you pruchase from the lounge attendant, that might be different.
You do realize that meals in the dining car are generally excellent, if a bit expensive? If you are making do with Pop-Tarts for breakfast, I would strongly suggest you try at least breakfast in the dining car (not the lounge car). That meal is not quite so expensive usually, but gets your day off to a much better start - and the food is quite good. You may be surprised, actually.