Ahm, in the manga Rem kills L too.
He dies because they think Misa is the second Kira. Sooner or later they would get proof and she'd be sentenced to death. An because of that they threaten her life. So Rem dies when he kills them.
In the movie L is only pretending to be dead as far as I know. But I haven't seen part 2 yet so I can't explain that in detail.
"For Feanor was made the mightiest in all parts of body and mind, in valour, in endurance, in beauty, in understanding, in skill, in strength and subtlety alike, of all the Children of Illuvatar, and a bright flame was in him"