I've tried it with Crafty Cuisine and Grillin Galore and no foods from there can be putted in backpack. If included compability is not an option, I want to suggest creating a config to ad IDs of food that can be putted in lunchpack

There is a tag that can be used to add custom foods: https://github.com/fzzyhmstrs/piu/wiki/Item-Tags. You can also use the c:foods tag