Now that we've determined that prayer effects and transforms us, the one who prays, we can turn to the Letter's second question, "how important must a need or desire be before we can properly make it the subject of a petition?" Perhaps we should just ask God for big things, like that you should always be healthy and that your kids should be well behaved, or global things, like world peace and to remove hunger.
Lewis pushes back on this. First, he notes that this is inauthentic. If you don't speak your mind, you're not standing before God in a true and vulnerable fashion. It's like you're trying to hide something from Him. Second, laying it all out in prayer is transformative, and will help you understand what is most and least important.
As it happens, I am currently reading R' Yehuda Amital's "L'Olam yehai adam, - Always one should be man," and in his section on prayer he says as follows. If you were sitting right next to R' Aharon Lichtenstein (R' Amital's co-head of Yeshivat Har Etzion), and needed a pencil, you would never ask him to borrow one. Not because R' Lichtenstein wouldn't let you (of course he would!) but because you would think it's too trivial a request for someone of such great stature. God, however, should be approached with any request no matter how small.
I might push even further and say that it's especially important to put the little things before God. It's obvious that no one has complete control over their health, and few people are brazen enough to think they have complete control over their wealth, or that they will never sin. It's obvious to everyone that those looming issues are in God's hands and must be put before Him. However, sometimes we might trick ourselves into thinking we can control the smaller thing: the test we've really studied for, the work presentation we know we've mastered. Perhaps, God forbid, we might think we can do those without His help. By formulating them into our prayers, we force ourselves to recognize that we have no agency whatsoever without Him. Even things we think we have in control are completely in His control.
So I would suggest that especially the small things, the things we don't consider much of a need, should be put into prayer to enable us to realize Who is really the one who determines and fulfills our needs.