I say not. If someone truly believes that it is the moral thing to do to kill someone they love, then let them do so, there is no prior restraint. But once it is done, they will be held accountable, and should be brought in front of a jury.
I don't think there is much appetite to punish such crimes, certainly not to the full measure or anything close that is allowed by law, and juries need to bear in mind that they are free to find someone not guilty, even when they think that he is. And after that you're only facing our wishy-washy judiciary, so you will have a fair chance of getting away with it, if it seems like a genuine mercy killing.
That is as good as it should get. No one should be given a licence to kill, and I am not at all sure that someone can consent to their own death, in strictly legal terms. Leaving the law as it stands leaves the weight where it ought to be - prohibiting the taking of a human life. As such, only those wholly convinced of the rectitude of taking such a serious step will proceed. Changing the law, in any case, will not remove the necessity of investigating such events.