In addition to Definition 24, I also find 23 somewhat helpful:
intr. Dicho de una parte o porción de algo que se reparte entre varios o les es común: Caber o pertenecer.
If you are playing a card game or a board game, and someone loses track and doesn't realize it's his turn, you could say:
José, te toca.
Which means, José, it's your turn, or, the turn order has gotten to you.
If you are cutting up a cherry pie into equal portions, and one child complains that he didn't get enough, you could say:
A cada quien le toca la octava parte.
Which means, everybody gets one-eighth, or, one-eighth goes to each person.
Your sentence is similar. I would think of it like this:
We lived through that.
For example, if my son is studying the Vietnam War era, I might sadly tell him, "I lived through that." Meaning, that war was my turn to live through. Whereas my mother lived through World War II.