I'd like to address the "to a Christian" aspect of the question (I'm not sure the "to a non-Christian" aspect is on topic). I would argue in favour of assisted suicide, on a case by case basis. I don't intend to comment on whether it should be legal or illegal, because I think that is mostly irrelevant to the issue of its morality.
The Bible doesn't have anything directly to say about assisted suicide, or therapeutic relentlessness, so any Christian viewpoint on this subject must be an inference from more general principles. I argue that OP's question is a subset of the more general question of "Is it ever okay for a Christian to choose death?"
Is it ever okay for a Christian to choose death?
One response by Christians to assisted suicide is that we do not belong to ourselves, and thus do not have the right to choose death. My problem with this argument is that it is too black and white. What about martyrdom? We ought to be willing to give up our lives for the cause of Christ, which in many cases (such as refusing to denounce Christ at gunpoint) is effectively suicide. So clearly there are some cases when it is okay to choose death.
I'd argue that the principle at work in whether choosing death is moral is whether the benefit of death outweighs the cost.
There is no cut and dry answer of whether choosing death is always okay, or never okay. Like most aspects of Christianity, legalism doesn't work - we must each examine our own hearts, and the Spirit's will for us.
So, what are some examples of Christians choosing death, where the benefit of death outweighed the cost?
Countless martyrs throughout history have chosen death for the sake of the gospel. In those cases, the benefit (furthering the gospel, integrity in not denying Christ) outweighed the cost (momentary death).
The Bible also has several examples of people choosing death when the benefit outweighed the cost.
One example is Samson:
Judges 16:30-31 (NIV)
30 Samson said, “Let me die with the Philistines!” Then he pushed with all his might, and down came the temple on the rulers and all the people in it. Thus he killed many more when he died than while he lived.
31 Then his brothers and his father’s whole family went down to get him. They brought him back and buried him between Zorah and Eshtaol in the tomb of Manoah his father. He had led Israel twenty years.
Samson acted as he did, knowing it would kill him. But the benefit outweighed the cost, as he was able to take many Philistines with him, and was likely going to die soon anyway. Note that whether we think killing Philistines is a "good thing" is irrelevant. It apparently fit into God's will and plan, or God would not have given Samson strength to do so (the context suggests that God gave him the strength).
Another example is Jesus. Certainly Jesus could have prevented his death
Matthew 26:53 (NIV)
53 Do you think I cannot call on my Father, and he will at once put at my disposal more than twelve legions of angels?
But he considered doing the will of his Father (Mark 14:36) and the "joy set before him" to outweigh the cost:
Hebrews 12:2 (NIV)
2 fixing our eyes on Jesus, the pioneer and perfecter of faith. For the joy set before him he endured the cross, scorning its shame, and sat down at the right hand of the throne of God.
Now, some might argue that Jesus knew he would be resurrected, and thus was not choosing death. But don't we as Christians have that same assurance? As Christians, death is not the end. In fact, it is far better to die and be with Christ, but we ought to remain when the cost of death outweighs the benefit.
Of course, for Christians, since we do not love our worldly life, the cost for us is little and the benefit for us is great. But remember that we are called to love, and we must take into our calculation the cost for others and the benefit for others that can be incurred by our remaining in the world. For if all Christians were to simply off themselves, there would be no evangelism. Paul dealt with this very struggle, and his cost-benefit analysis led him to remain:
Philippians 1:21-25 (NIV)
21 For to me, to live is Christ and to die is gain. 22 If I am to go on living in the body, this will mean fruitful labor for me. Yet what shall I choose? I do not know! 23 I am torn between the two: I desire to depart and be with Christ, which is better by far; 24 but it is more necessary for you that I remain in the body. 25 Convinced of this, I know that I will remain, and I will continue with all of you for your progress and joy in the faith,
So when does the benefit of death outweigh the cost? There are probably a few clear cut cases, such as if the person is a vegetable with no chance of recovery. Let that person be with Christ.
But generally, it depends on tons of factors, such as the amount of suffering one is in, the remaining time left in life, the possible benefit one might have to others, etc. Christians should prayerfully examine their own hearts when making such a decision, and remember the importance of loving others in their decision. We shouldn't automatically choose death, simply to escape suffering, when our life may benefit others or further the gospel. Rather we can count our current suffering as joy, knowing that we are choosing it for the sake of love and the gospel, and we will surely be rewarded.
So, when is it okay to assist in choosing death?
Well, first of all, if we assume the morality of the chooser's choosing, then I don't think the assistance should be categorized as a sin. I don't believe it falls under murder, as the motivation is love, rather than hate. In the same way, an accidental killing is not murder (i.e., a car crash), because the spirit of the law is concerned with our intentions, and our heart (Matthew 5:21-22).
One caveat is that we should never assist in the death of an unbeliever. For the unbeliever, we need to hold out fervent hope that he will come to Christ before his demise. Though the unbeliever does not realize it, the benefit of relieving temporary suffering never outweighs the cost of missing out on the chance to come to Christ.
In my opinion, in most assisted suicide cases the benefit of death does not outweigh the cost, but I am unwilling to make a blanket statement against all assisted suicide. I'm sure that there are cases where a Christian's suffering is great enough, and their remaining time is short enough, so that the relief from suffering outweighs the benefit they might have on others in their short remaining time.