It is believed by some that L never dies in the movie L: Change the WorLd, despite Ryuk suggesting so. The evidence highly refutes this theory.
This is believed for several reasons, the main one being that the series is a spin-off, and therefore not all of the rules from the anime and manga may apply, such as the one about burning a Death Note not being able to stop a person's death. Another reason this is believed is because Ryuk appeared extremely nervous when L was about to burn the Death Note, trying to think of an excuse after L stated that he would burn the Death Note anyway. The final reason this is believed is because at the end of the movie, L states that he wants to live a little longer, possibly eluding to him not dying.
Rem quite clearly caused the deaths of both L and Watari in an effort to preserve Misa's life, and in sacrifice of her own. L being the intelligence behind solving the case