People who do not believe in God or religion can surely lead ethical lives. But they cannot lead holy lives. By definition, the ideal of the holy, as understood by Judaism and Christianity and that unique amalgam known as Judeo-Christian values, needs God and religion.
Here is the best way I know of to explain holiness in Judeo-Christian religions: There is a continuum from the profane to the holy that coincides with the dual bases of human creation -- the animal and the divine.
The human being can be said to be created in the image of God and in the image of animals. We are biologically animals, and we are spiritually, morally and theologically God-like (at least in our potential). God is the most holy; and animals, as helpful, loyal and lovable as many are, are at the opposite end of the holiness continuum. This is in no way an insult to animals. Saying dogs and lions are not holy is no more degrading to them than saying men are not women or women are not men. That is how they are created.
There is actually a secular way to understand this. If we saw a person eating food with his face in a bowl, we would think, "He eats like a pig" or "He eats like an animal." That is an insult to a person -- because humans are supposed to elevate their behavior above the animal (this is a goal of Judeo-Christian and just about every other major religious tradition). But it is no insult to an animal. When an animal eats face-first out of a bowl, we hardly think ill of it; but when a person mimics animal behavior, we do think lower of that person. So, even non-religious society has imbibed some of the view that acting like an animal is not how a human being should generally act.
Now, to better understand this, one needs to appreciate that holiness is not a moral category. There is nothing immoral in eating with one's face inside a bowl. It is unholy to do so, but not immoral or unethical.
It is crucial to understand the difference between the moral and the holy. Even many religious people blur the distinction by labeling unholy actions immoral actions. And that has often given religion a bad name because thinking secular people know that some actions called immoral by the religious are not necessarily immoral.
This is particularly true in the sexual arena, where many religious people characterize unholy behavior as immoral behavior -- so much so that the very word "immoral" has come to be equated with sexual sin.