One idea could be that Naruto and Sasuke are somehow transported to the world of Kill la Kill. They might get involved in the fight against the Life Fibers, with their ninja skills being a unique addition. Maybe Naruto's Rasengan could be used to disrupt the Life Fibers in a new way.
One reason could be Sasuke's thirst for power. If he believes Naruto is the only obstacle in his path to ultimate power, he might be driven to kill him. In some fanfictions, Sasuke may be influenced by a dark entity that twists his mind into thinking Naruto is a threat that needs to be eliminated.
In some cases, Sasuke could be angry. He might see Naruto's request as a sign of weakness or as Naruto giving up too easily. He could lash out at Naruto, telling him to fight instead of asking for death. However, he would still be deeply troubled by the request and would probably struggle with it for a long time, constantly thinking about whether or not he should consider it.
Naruto might initially be shocked and confused. He has always considered Sasuke as a friend, so Sasuke's sudden attempt on his life would be a huge blow. He may try to talk to Sasuke first, to understand why he is doing this.
One possible reason could be that Sasuke might have gone too far in his pursuit of power even after the war. He could have been a threat to the newfound peace in the ninja world, and Naruto, as the protector of peace, might have felt he had no other choice.
Naruto might be very friendly and curious about the characters from Kill la Kill. He could try to befriend Ryuko immediately and ask her about her cool outfit and powers. Sasuke, on the other hand, would be more cautious and might see them as potential threats at first.
One possible motive could be if Sasuke was on a path of destruction that endangered the entire ninja world. Naruto, as the protector of peace, might see killing Sasuke as the only way to stop him. For instance, if Sasuke was about to unleash a powerful and uncontrollable jutsu that would wipe out many innocent lives.
Perhaps in a fanfiction, Sasuke discovers a new and extremely dangerous power that he can't control and it starts to endanger Konoha. Naruto tries to stop him but in the heat of the battle, accidentally kills him. Overwhelmed with guilt and feeling that the village will never understand, Naruto leaves. But this is a very different take on their relationship and the Naruto world as a whole.
One idea could be a crossover where Naruto and Sasuke are somehow transported to the world of Akame ga Kill. They could team up with Akame and the Night Raid members to fight against the corrupt empire in that world. Maybe Naruto uses his shadow clones to gather intelligence, while Sasuke's sharingan helps in combat against the powerful foes.