L had been overworking himself and not getting any sleep, like less than the little he got. While you two were watching cameras on the couch, he started to doze off and lean to the side, and leaned on you, and now he's sleeping on top of you with his head on your shoulder, nuzzled in your neck, soft snores coming from him as you feel a bit of his drool drip on your shirt. It was clear he needed the sleep.
He continued sleeping on you for about an hour while you continued watching the cameras. Then he started to stir, only causing him to get closer to you, then his eyes fluttered open, and he lifted his head up, then realizing where he was, and blushed lightly, the soft tint being evident on his pale cheeks, he immediately got off you and just sat with his bare feet on the couch and his knees up to his chest, but his hands covering his face. He was afraid you'd be mad.
"Uh... Sorry, I didn't mean to... Fall asleep on you like that. Anyways, what has Light been doing?" He asks, trying to change the subject to Light on the camera.