One explanation is that the KJV translation of the Lord's Prayer, which English-speaking Catholics still insist on using today, is misleading. The translation should really be: "Subject us not to the trial, but deliver us from the evil one," or something like that. Although I lack the specialized scholarly knowledge to know which translation is the best, the original does seem vague enough to admit more than one translation that would, inevitably, be interpretation. After all, the original Greek itself is a translation of Jesus' Aramaic. The alternative translation I've just cited is certainly one such interpretation. The idea seems to be that it's not just any old temptation we are to ask to be spared; it is obvious that none of us past the age of reason are, or are going to be, spared temptations. We are asking to be spared the sort of naked confrontation with Satan that nobody with the slightest idea of what that would mean would desire. I think that's true; but it can't be the whole story, and in fact it only heightens my puzzlement.
For such a confrontation is exactly what Jesus had in the desert; and he is our exemplar as well as our savior. Such confrontations were well-known to the desert fathers and mothers who were the progenitors of monastic spirituality. Indeed, the more serious one is about transformation in Christ and acts accordingly, the more likely one's ascesis is to occasion such a confrontation—or an experience enough like it as to make no difference. The lives of many saints confirm that. So, does the Lord's Prayer petition that we be spared something that is likely in almost direct proportion to our spiritual progress? I can't help thinking that unlikely.
Another explanation I know is the Thomistic one, which Tom Kreitzberg of Disputations expounds well today with appropriate references. St. Thomas distinguishes, rightly, between temptation in the sense of "testing," as in trials that test one's virtue, and temptation in the sense of "solicitation to evil." Clearly, God doesn't do the latter, because he cannot; so it would be unreasonable to interpret the petition in the Lord's Prayer as asking him not to do it. But does the petition really seek exemption from testing? Well, nobody beyond the age of reason is exempt from trials that test their virtue. I've had some; I've failed some. (Okay, most.) Being enjoined to ask for what one knows isn't going to be granted doesn't seem rational; and Jesus was, among many other things, rational. So, what does St. Thomas have to tell us that doesn't just reduce to the previous explanation?
According to Aquinas, "God is said to lead a person into evil by permitting him to the extent that, because of his many sins, He withdraws His grace from man, and as a result of this withdrawal man does fall into sin."
In other words, the petition amounts to, "Do not abandon us when we are tempted to sin." It is a way of praying for the promise St. Paul records in 1 Corinthians 10:13: "God is faithful and will not let you be tried beyond your strength; but with the trial he will also provide a way out, so that you may be able to bear it." By petitioning God to do what He has promised to do, we draw our own hearts, minds, and wills closer to His.
The difficulty I find here is not with the conclusion Tom draws, which is true, but with the premise Aquinas lays down. I do not believe that God "withdraws" his grace from anybody, for any reason. We are all, always, given grace sufficient for passing the really big tests. If God's grace abandons us, it is because we have already chosen to abandon it. When God chooses not to override that choice, that is respect not withdrawal.
Here's the explanation I prefer. Unlike us, Jesus was incapable of sin; hence, having nothing to fear from temptation himself, he was led to experience it so that his successful resistance would strengthen us to succeed too. Indeed the entire Paschal Mystery, of which Jesus' temptation in the wilderness was an important part, suffices to provide us with the necessary strength for the temptations (in both senses of 'temptation') we will inevitably face. But it would be presumptuous of us to assume we would abide in his grace manfully enough to be guaranteed success. So, when we pray that the Father not lead us where the Spirit led Jesus, we are not asking God spare us something which he manifestly does not spare us. If we are sincere, we are performing an act of humility by which we avail ourselves of Our Savior's infinite strength.