to break out (v): 7. To present something for use, especially something that had been stored out of sight or concealed.
In this context "break out" means to take out the food that had been stored somewhere (presumably in lunch boxes or come other container). By itself it doesn't mean "to eat", and it doesn't have to be used only for food:
We walked all day, following the map to where the treasure was hid. Arriving at the spot, we broke out the shovels and picks and proceeded to dig.
Similarly, "turn to" has multiple meanings. In this case, the closest is:
turn to (v): 4. To devote or apply someone or something to someone or something.
In this context it's short for "turn our attention to", meaning we focused on eating lunch. Again, nothing in the verb explains how we got lunch, only that lunch was the objective.