Would L personally kill Misa?
Rem's death doesn't make any sense unless L would personally kill Misa.
The rule is as followed;
''If the god of death decides to use the Death Note to kill the assassin of an individual he favors, the individual's life will be extended, but the god of death will die.''
But L was just busy exposing Misa as Kira or as the second Kira, which would result in her being sentenced to death, in no way shape or form was L her ''assassin'' so therefor Rem shouldn't have died when killing L.