In his debut, Luigi recieves a letter from Princess Peach saying that he and his older brother Paper Mario have been invited to Peach Castle for a clebration. However, just as they went inside, Bowser's forces had stormed their way into the caslte and had lifted it up high in the sky. It unseen, but Luigi does manage to escape the castle just before it takes off. Once Mario makes it back to Toad Town, he can visit Luigi anytime he wants in his house.
Super Paper Mario
In Super Paper Mario, Paper Luigi gets brainwashed to fight against his brother, Paper Mario, calling himself Mr. L. Paper Luigi does not have any memories of being Mr. L, after being reverted to Paper Luigi.