One common theme is loneliness. Chrollo often seems isolated in the original story, and fanfics tend to explore how his past experiences, like losing his family or being an outcast, led to this loneliness. Another theme is power - seeking. Fanfics show how his past traumas made him strive for power as a means of survival and control.
One great 'Chrollo Lucilfer backstory fanfic' is 'The Origins of Chrollo' on FanFiction.net. It delves deep into his early life, exploring how he came to form the Phantom Troupe. The author does a great job of showing his motivations and the events that shaped him into the character we know in the original series.
One possible moral could be about the importance of kindness. If the kid in the story shows kindness to the lion kid, it might teach that being good to others, regardless of their appearance or power, can lead to positive outcomes.
I'm not sure of the specific full story without more context. It could be a case of a bully targeting a vulnerable blind child, which is extremely cruel. There might be underlying reasons like the first kid having some behavioural problems or being influenced by a bad environment.
There are two central characters in the 'the kid and the lion kid story'. One is simply a kid, who could be a human child or perhaps a young goat (as 'kid' can have different meanings). The other is the lion kid, which is a young lion. Their relationship and the events that occur between them form the core of the story.
Perhaps the kid is from a foreign land that Naruto visited during one of his missions. The kid could be an outcast in his own place because of some unique trait. Naruto, being the kind - hearted person he is, decides to adopt him. It could be that the kid has a different kind of chakra or a strange mark on his body that makes others afraid of him, but Naruto doesn't care.