I wish that I had more general knowledge of the time to help create a clearer idea of the question. I know that the house of Saud arose in the wake of the Ottomans and that T.E. Laurence was instrumental in helping support Arab independence. Yet, I have never heard of any connection between the two. Was T.E. Laurence aware of the Wahhabist ideology of the Saudi dynasty? Was the support of the Sauds something that the British did behind the back of Laurence? I'd really appreciate any information I can get on this. Also, as an aside, I'm really impressed with the work that many of the responders do on this sub. You guys are great.
You haven't heard of any connection between the two because TE Lawrence was no fan of the House of Saud and did what was within his power to thwart its ambitions.
During WW1, Lawrence operated in the Hejaz region of the Arabian Peninsula, a geographically and politically distinct region, historically more cosmopolitan and diverse than the desert interior from which the House of Saud arose. Home of the Two Holy Places of Islam, Mecca and Medina, the Hejaz was the domain of the Hashemite dynasty, at that time headed by Sharif Hussein ibn Ali, and it was his cause that Lawrence worked to advance, often against his instructions from London and Cairo. At the time various wings of the British military and diplomatic bureaucracy were pursuing different objectives in the Arabian peninsula, and Lawrence's efforts in the War Department and the Egypt Office were running up against those of the India Office, which backed Abdulaziz ibn Saud. After the war, Lawrence was sidelined and open conflict over the Arabian peninsula erupted in which the Hashemites were largely abandoned by their supporters inside the imperial machinery, while Ibn Saud continued to recieve military support.
Lawrence was well aware of the ideology of the House of Saud: in response to an India Office intelligence bulleting promoting them as future clients he wrote an essay in which he described Saudi Wahhabism as unrepresentative of Islam as its reforms had "all the narrow minded bigotry of the puritan". If Saudi Arabia prevailed, he foresaw that "we would have in place of the tolerant, rather comfortable Islam of Mecca and Damascus the fanaticism of Nejd... intensified and swollen by success". Needless to say, this warning wasn't enough.
Source: Lawrence in Arabia: War, Deceit, Imperial Folly and the Making of the Modern Middle East, Scott Anderson