Reading "Mere Christianity" and having a hard time with book III, chapter 12

I'd hope that Lewis would give me at least a passing mark if I suggested that it was reasonably well summarised by this verse from a hymn by Helen Lemmel.

Turn your eyes upon Jesus
Look full in his wonderful face
And the things of earth will grow strangely dim.
In the light of his glory and grace.

Lyrics here

Hillsong doing a reasonable job of imparting the impression of

" ... They are too busy looking at the source from which it comes. But this is near the stage where the road passes over the rim of our world. No one's eyes can see very far beyond that ..."

He seems to be describing the bliss of faith where the knowledge of good and evil does not dominate our awareness. He does it kind of poetically. As we are sinful and not absolutely sure of our forgiveness, due to want of faith, the glory of Christ is hard to look at directly. We do not have such strong faith on this side of heaven not to be frequently taking our spiritual temperature. We are not so confident in the power of Christ's atonement as we aught to be. Therefore we still walk about thinking our sins are carried by ourselves and this makes us feel guilty and uneasy. The kingdom of heaven takes us to another world where sin and its horrors are no longer on our mind. Unfortunately we experience this grace imperfectly in this world. This does not mean that we can't peer into the land of grace by faith. Lewis just admits its heavenly and that others can see it better than he can.

Lewis' point is that while many Christians are focussed largely on the question of how they might avoid sin, and how they might be more moral, those who are more advanced in the faith are not thinking about those things at all. As they come to realize more completely that Jesus has paid the price of forgiveness for them, they stop thinking about those things. Instead they focus on Jesus, "the source from which it comes". They think about him, and about their relationship with him, and what he has done, and his love for them, and their love for him. In doing so they unconsciously still do the things that Jesus wants them to (what we call 'goodness'). In the very last line he opines that at this stage the Christian is usually close to passing on to be with Jesus and no longer in this world.

This is a fairly straightforward reference to the teaching that once saved, God works on us to make us more Christ-like. (More here) This is a very common belief, in mainstream Christianity, and in not-so-mainstream denominations, such as the LDS Church. It is also known as Sanctification.

Progressive sanctification

"Indeed, the more sanctified the person is, the more conformed he is to the image of his Savior, the more he must recoil against every lack of conformity to the holiness of God. The deeper his apprehension of the majesty of God, the greater the intensity of his love to God, the more persistent his yearning for the attainment of the prize of the high calling of God in Christ Jesus, the more conscious will he be of the gravity of the sin that remains and the more poignant will be his detestation of it....Was this not the effect in all the people of God as they came into closer proximity to the revelation of God’s holiness." -John Murray, Redemption Accomplished and Applied

The first paragraph you quoted alludes to the experience that in the beginning of our Christian walk, we all think about the rules a lot. We think about avoiding this sin, trying to increase this positive trait. As we become more conformed to the image of Christ, these things become more natural. Our minds become more confirmed to the image of Christ through God's continuous work on us, and our own submission to His will that we no longer think about nit-picky rules, but instead, simply live in a way that is more Christ-like. We don't think about it, we don't verbalize it, it becomes who we are.

In the end, we're not thinking about being good, we're too busy focusing on Christ Himself, the source of all goodness.

The last few sentences are indicating that Lewis didn't think he'd reached the same point in his walk as other, who were more closely confirmed to God's image than he was.

Taking this a step further, it is a quite lovely way of saying that Christianity isn't about rules, regulations, or morality, it's about Christ, and our relationship to and with Him. We are "good" (or at least as good as we can be) because of the work He does in us, not because of our obedience to rules, but because of who we are through Him. Our morality is based on our love for Him. This is discussed here.