I don't own Death Note.
Sometime after the death of Raye Penber and his fiancée, Naomi Misora, the Japanese police began to distrust L leaving only a few members active to hunt down Kira. However, knowing that L himself will be putting his life on the line, he will do whatever it takes to bring Kira to justice.
Standing up while slouching, the young detective slowly walks into his daughter's room. Finding the two-year-old sleeping peacefully in her bed, L gently pets her chocolate brown hair and then kissed her forehead before leaving the room.
Even though his daughter would only be raised by her mother if anything happens to himself, the least that the insomniac father wants to do was to put his own family in danger.
"Seychelle, if I were to die during the Kira investigation, tell Elle that I loved her very much and that she should not be discourage of becoming a detective because I know that one day she'll surpass me," the young detective spoke to his wife.
"Of course, after all she does carry the blood of the first Watson," Seychelle was confident.
"I'll have to get going. Good night."
"Night," the fourth Watson kissed her husband.
I won't let you die.
Xxx
With only six remaining members of the Japanese police, L invites them to his hotel's room. Much to their surprise, they did not expect him to appear as a young man with a disorganized appearance. As the Kira case remains ongoing, L continues discussing about the killer with the team.
Assuming that this story follows the same as in the anime and manga, I would write another story focusing on L's daughter and wife while he's away.