I really think this is the wrong interpretation of the end of that movie.
In the movie, Lawrence tries to resolve his apparent split loyalties by bringing the Arab and British interests into alignment and has a couple of initial exhilarating successes, but he ultimately fails, badly. Neither the Arabs nor the British live up to his idealistic expectations. The British use him in ways contrary to his intentions. He also discovers that his own idealism is compromised by his egotism and sadism.
The beautiful, dramatic desert landscape, the danger of Lawrence's mission, the high political stakes for the Arab tribes, and the historical context of war all help create an illusion of the possibility of heroic transcendence that is deeply inspiring, but in the end, it is all human and mundane: human vices at the small scale and human politics at the large scale. There is no transcendence.
I can see how some people walking out of the theater might have only remembered the feelings stirred up by the beautiful cinematography and the epic score, and forgotten absolutely everything else, but I think it's a better movie for sweeping the viewer up into that feeling before dropping them down into the political squabbling, betrayal, disappointment, and tragedy.
Not to mention the scene where he tries to pass as an actual Arab, the results of which aren't those of a stereotypical "white savior" story.
I can't really say it's not a "white savior" story but it's a subversive enough take on it that I'd recommend it to people who are turned off by white savior stories. The movie has much more depth than that.
I don't know why it is considered politically incorrect nowadays to say that the world as we know it was shaped by white people. Deng Xiaoping himself constantly told his own comrades how fucking pathetic China had become. And nobody could argue with him.
Its only Lawrence himself who romanticizes his own journy and hopes preserve some form of democratic nationalism. Only to be then synically stabed in the back literally everybody, the tribal leaders, the english politicans and of course the arab rules.
My favoirte part of the movie is when the english leader and the arab rules both agree that its good that he is finally gone. This is the origin of the modern battle inside of the middle east between islamic populism (muslim brotherhood) and ruling dynasties (Saud).
The movie made this very clear and expicite, and Lawrence himself knew that this was his role, even when he tried to do the best he can for the people he liked within these constraints.