To recap my points from here:
1.) In the same work Timothy Keller was quoting (which TK should have recalled since it’s one of the few times Lewis wrote strongly in favor of divine persistence to save), Lewis first repeatedly argued and stressed that as Christians we should not expect God to give up on saving sinners. But then later, in the portion quoted, Lewis decided this meant God is forced to give up by the sinner, being defeated by the sinner on His purpose to save them from sin.
1.1.) It’s rather amazing that TK (the Calvinist Presbyterian, not the Arminianistic Cumberland Presbyterian 
) would quote that since Calv theology is absolutely against the idea that God is defeated by sinners in saving them from sin; much less that God would simply choose to give up even though He would succeed if He kept trying. Calvs explain final perdition on the ground that God never chose to save some sinners from sin at all. When he says (as in the headline for his website) “you are more sinful and flawed than you ever dared believe, but more accepted and loved than you ever dared hope,” he means all-of-you-inclusively for the sin and flaws, but then switches immediately to only addressing the elect in the second half of his sentence, those whom God has chosen to save from their sins. That isn’t necessarily “you”, it’s only ‘maybe you’. Lewis was the opposite of that: he definitely meant “you” both ways, but didn’t really mean “you” were more loved by God than “you” ever dared hope. Otherwise he would have at least dared to hope that all “you” would be saved. But he didn’t.
(Or rather, they both do mean all inclusively in both ways sometimes, but not consistently so – or they’d be, or would have been, Christian universalists. But part of their appeal is that they do both apparently promote the gospel assurance of total scope and also the gospel assurance of original and victorious divine persistence.)
1.2.) But this also runs against the thrust of Lewis’ argument earlier about divine persistence, which was that we should expect from God’s nature both that He would act to save everyone and also that He would persist until He gets it done. Nor was it a question of God being “obligated” to do so by moral appeal to a standard higher than God: Lewis based it (though admittedly not very clearly) on God’s trinitarian characteristics. This is why Lewis thought God was forced to quit; but in doing so he still ended up disavowing his own principles about why we could expect God to keep at it. He should have concluded, if God never saved some sinners, that God still keeps at it in a never-ending stalemate. Though even that would run against his emphatic insistence elsewhere that God is competent to win the chess match, an analogy which doesn’t obviate the free will of the opponent at all.
1.3.) Despite Lewis’ insistence there that God sadly quitting and letting sinners lock themselves into annihilation (more or less) had the authority of scripture behind it, there is nothing in scripture about God sadly quitting. Timothy Keller on his theology ought to be even more strongly against that; and Lewis shows elsewhere he does know better than that: God actively punishes sinners so long as they remain impenitent. (You yourself were quoting scriptures showing God’s active punishment of sinners.) Similarly, sinners can’t annihilate themselves: if any are annihilated, God actively chooses to do that, by choosing to withdraw His ongoing action by which they have continued to exist up to that point.
2.) You (or whoever you were reading, be it Lewis or Keller or whoever) were appealing to the principle of accepting whichever soteriology involves the most fairness. (“What could be more fair than that?” etc.)
I am 1000% in favor of that approach. Which is why, on that principle, I reject Lewis’ notion (per soft Arminianism) of a final victory of unfair people insisting on being and remaining unfair and never coming to be fair.
I also on the same principle reject the harder Arminian notion of God deciding to authorize final unfairness by choosing to give up empowering and leading unfair people into being fair people.
I also on the same principle reject the Calvinistic notion that God chooses never to empower (much less lead) some unfair persons to being fair, but instead actually creates them unfair and by His choice ensures they remain forever unfair (until He annihilates them or not).
What glorifies God more? For some sinners never to come to glorify God by their triumphant choice? For some sinners never to come to glorify God by God’s authoritative choice? For some sinners to come to falsely glorify God, while remaining rebels in their hearts, by God’s authoritative choice? Or for all sinners to come to truly glorify God, in cooperation with God’s choice?
Even if some unjust/unfair people never come to do justice, and never come to properly glorify God, no one anywhere in any way can coherently argue that that results in the most conceivable fairness, justice, and glory to God. The moment authors appeal to that to supposedly bolster their argument for final perdition, you should recognize they’re making at least one highly important and inconsistent mistake somewhere.
This is aside from any discussion of the scriptures you cited, which I and others have discussed in much more detail elsewhere (and which at the time you agreed with the results of those more in-depth discussions about). At the very least, they do not describe the hell of C. S. Lewis. Which was a main reason why I always had at least a few nagging problems with his approaches and arguments on that topic.
