Crossing the Spiritual Rubicon
Now for the quick and dirty explanation:
Animism, it could be argued, is humanity's most natural* means of viewing the world. For the animist, the material and spiritual worlds are intertwined to the extent that they're essentially indistinguishable. There's no separation of meaning and object. The gods are present in everything. The religions of civilization are abstractions of animism. Early on, the gods are separated from things, commanding them from the heights so to speak. Later the gods are fused into the concept of God to the point that in medieval times God and the divine represent a separate world altogether.
However, the Beduin tribesmen that Lawrence dealt with, while monotheistic in terms of believing in one God, were quite animistic in their approach. Here's how he puts it:
"The Beduin could not look for God within him: he was too sure that he was within God. He could not conceive anything which was or was not God, Who alone was great; yet there was homeliness, an everyday-ness of this climatic Arab God, who was their thoughts, their familiar resource and companion, in a way impossible to those whose God is so wistfully veiled from them by despair of their carnal unworthiness of Him and by the decorum of formal worship."
Keeping that in mind: Enter rationality, science and technology. Here God is even more abstracted and, as rationality and empirical investigations march on, God becomes increasingly unnecessary in terms of explaining our existence. By Nietzsche's time, the notion of God has become philosophically absurd and, in light of advances since then, has become doubly absurd.
Yet this complete severance from our animistic roots is, in a way, tragic. Much is lost and there's no going back. To try only creates a parody of belief, a farce, a veiling of what we know in our bones to true: The God we want to worship isn't there.**
Lawrence sensed this. Yet he was drawn to the Beduin's naturalism - the wholesomeness, the meaning and the integrity of their view of life. He could master their language and adapt to their culture but he could not be it. His admiration fueled an ambition to lead the Arabs to their own modern state. But this was contradictory: Lawrence was leading the Beduin across a Rubicon that he himself wished he could cross back over.
*I use "natural" in a qualified sense here. Ultimately there is nothing that isn't natural.
**Here I'm referring to God as transcendental, anthropomorphic, patronly overseer who stands outside of nature and directs things. Martin Buber made an excellent case for believing in an anthropomorphic God: Even though the idea is absurd intellectually, believing in a personal God was the only way he could see to develop an I-Thou relationship with the greater reality out there. We are only equipped to do it this way, Buber asserted. I contend that once the spell is broken, intellectually or otherwise, you can't conjure God up again and take Him seriously. The practice becomes delusional, conflicted and dogmatic.