Perhaps a fanfic where L is at the bottom of his game, almost defeated by Light. But then he finds an unexpected ally in a character who was previously thought to be insignificant. This ally has a unique ability that helps L turn the tables in their battle of wits over the Death Note.
A plot could revolve around the idea that the Death Note has a hidden power that only activates when the user is at their lowest point. L, being in a difficult situation, unknowingly triggers this power and has to figure out how to control it while still trying to expose Light as Kira.
You can explore his relationships in a new light. If he is at a low point, he might open up more to the people around him. In the fanfic, let him form a deeper bond with Watari or even a new character. Through these relationships, we can see his character develop, like learning to trust more or becoming more empathetic.
Some fanfictions might center around Baby L's first encounters with the criminal underworld. They could show his initial reactions to the complex and often dark nature of the crimes he would later be known for investigating.
One interesting Death Note L OC fanfiction could be where the original character has a unique ability to read L's thoughts. This adds a whole new layer of mystery and interaction between the two. Another could be an OC who is a detective from another country and teams up with L to solve Kira cases. There are also fanfictions where an OC is a childhood friend of L and has some secrets related to the Death Note.
The pairing of L and Misa is interesting because they are such different characters in the original 'Death Note' series. L is highly intelligent and logical, while Misa is more emotional and impulsive. In fanfics, seeing how these two contrasting personalities interact and potentially develop feelings for each other is fascinating.
A crossover with 'Fullmetal Alchemist' could also be fascinating. Maybe Edward Elric discovers the Death Note in his search for the Philosopher's Stone. He would be conflicted because his moral code as an alchemist goes against using such a tool for killing, yet the power it offers could potentially help him achieve his goals in a different way.
There might be a fanfiction where L discovers Light's identity as Kira much earlier, but instead of immediately trying to expose him, he decides to study Light's motives and actions more closely. This could involve some intense psychological battles between them as L tries to figure out what makes Light tick and Light tries to outwit L in a different way.
Maybe the kidnappers are actually Kira supporters. They kidnap L because they see him as a threat to their 'god' Kira. L could use his deduction skills even in captivity. He might start a mental battle with his kidnappers, trying to make them slip up and reveal information about Kira's identity or their own motives.
Perhaps a story where the Akatsuki members from Naruto are intrigued by the power of the Death Note. They could try to obtain it for their own purposes, like achieving world domination in a different way. It would be interesting to see how characters like Itachi or Kisame would react to such a strange and powerful object that is completely different from their ninja techniques.
An interesting OC fanfiction could be about a Death Note owner who doesn't want to use it for evil but for good in a very specific way, like only targeting truly heinous criminals who keep escaping justice. They could have moral dilemmas throughout the story.
One plot idea could be Ryuk trying to save Light from the consequences of his actions. Since Ryuk is an otherworldly being, he might have some knowledge or power that could potentially help Light avoid getting caught. For example, he could use his Shinigami powers in a way that no one expects to mislead the investigators on Light's trail.