I hate to post spoilers, but the Old and New Testaments have several examples of wicked people who are never redeemed.
And again, hate to spoil the plot, but Satan is not redeemed either.
Tolkien is a weak thinker because he doesn't make room for redemption, thus, he is not a Christian. Look at Gollum - he sins, destroys his life, but where is the redemption, the need for god's absolution? None. A great thinker would've made Gollum the hero, to redeem himself.