[Pitchwife]

You're right, of course, to insist on Eru's absolute freedom at any given point. However, as he introduced the Children into the Music after Melkor's discord, I like to think he may have adapted his design of their nature so as to counter the effects of the discord and enable them to fulfil his purpose in a world marred in the making. Or maybe not - if he knew what Melkor was up to all along, he didn't need to adapt his design. But this is touching on the problem of divine providence vs free will, which is another can of worms.

As for re-inventing the theological wheel, as you've so kindly encouraged me to do, the crux of the biscuit is this:
Christian theology (at least the Catholic tradition I was raised in) tends to regard death as 'the wages of sin' - i.e. a lamentable consequence of the Fall, to be redressed by Christ's incarnation/crucifixion/resurrection (hence 'death, where is thy sting'); implying that if Adam & Eve had not sinned and fallen, they might have lived forever.
(Genesis itself is sort of ambiguous about this question; on the one hand, we have

you are dust, and to dust you shall return

(Gen 3:19 - God proclaiming judgment on Adam after the Fall); on the other hand (Gen 3:22-23):

Then the Lord God said, 'See, the man has become like one of us, knowing good and evil; and now, he might reach out his hand and take also from the tree of life, and eat, and live forever' - therefore the Lord God sent him forth from the garden of Eden

According to this, God banished Adam & Eve to prevent them from gaining immortality - which seems to mean they didn't have it before.)

For Tolkien, however (as far as we can judge from his writings), death was something completely different, namely 'the Gift of Ilúvatar': meaning, as I understand it,
1. part of the nature of Men as designed by Eru, regardless of any sin they may have committed, and
2. something that may have been tainted, but untainted its name would have been good (see above); which I take to mean that even if it's been tainted, it's still the best way for Eru to achieve the good he has in mind for Mankind.
To me, none of this sounds like orthodox Christianity. Now we know that Tolkien himself claimed LotR to be a thoroughly Christian book ('consciously in the revision', etc.) - which makes me wonder whether
a) there's any kind of loophole in Christian theology that allows for Tolkien's view of death to be considered as orthodox, or
b) this is a case of the truths of his heart prevailing over the truths of his faith.

(Athrabeth, with its story of the Fall of Men and preview of the Incarnation, looks like a late attempt by the Prof to make his mythology conform to the Christian tradition; but while it's certainly an interesting and touching piece of writing, I'm not sure that he was quite satisfied with it himself - or why else would he have said that parts of it sound like parodies of Christianity?)