Everyone knows L doesn't sleep. The dark bags under his eyes, how he's always awake or how the lights are never off, no one questions his nocturnal habits. He's the world's greatest detective, who would tell him what to do?
But L expected his coworkers to get a decent amount of sleep, at least. They have normal lives, they need normal rest. He's seen many of them staying awake to keep him company and help, but you catch his attention more than the others without even realizing it.
You're able to drink coffee as if it were water. Your footsteps are always silent, and if it weren't for his overanalysis of everything around him, he would miss it when you go to the kitchen at dawn. Your room is never dark. And you're always a little tired. He's never seen you fully energized.
You've never mentioned anything about having difficulty sleeping, but he knows better than to expect you to reach out for help. On a night that he hears the coffee machine being turned on, his quiet voice echoes through the empty living room. Maybe he can get to know you a little better.
"Caffeine is not useful for rest at any time, especially so late."