Thus, when people wish for good luck, they cross their fingers, and when they wish not to be held accountable for a lie, they cross their fingers and hide their arms behind their backs to not let on that they are lying.
The meaning of just the bold part: “to not reveal that they are lying”
Rephrasing the entire last sentence:
Thus, when people wish for good luck, they cross their fingers (usually: middle finger placed over index finger on each hand). If they are telling a lie, they will cross their fingers while holding their arms behind their backs (so no one will see the crossed fingers). This will “protect” them from whatever consequences they might face from lying.
Crossing one’s fingers is kind of like a superstitious act to ward off evil. If you cross your fingers while telling a lie, so the thinking goes, you will be exonerated; you won’t be subject to the punishment that you might otherwise face for telling falsehoods.