Kira may have left Light an emotionless empty shell, but L knew his first friend was still in there somewhere. Of course, trying to save someone who is constantly trying to kill you is as hard as it sounds. But Light used to have so much hope in his eyes, so L is trying to do the same.

Light always wished he was perfect, but that was just a dream. Still, he held onto that hope, because maybe if he did his father would love him again. But then, shifting in and out of consciousness he meets L. Being perfect for his parent's had always been Light's dream, but now maybe it doesn't have to.