I don't know a lot about Lawrence but I believe he spent some time in the southwest and saw what America had done to the indigenous population there. I'm guessing his views on the American psyche is heavily influenced by this experience so he's unlikely to give much consideration to the more positive aspects of the "essential American soul". He's said to have avoided visiting India, as he felt he would be "overwhelmed"; which, for a sensitive person who is coming face to face with the results of his countrymans oppression, would be a fairly reasonable response (India IS overwhelming!). He likely had more sympathy for MK Gandhi than Colonel Dyer. Lawrence's lack of sympathy for the American population is somewhat ironic in light of his sympathy for the oppressed "Indian"; considering that his country was once their oppressor.
To me, if one wants to understand the "essential soul" of a people, one is better served by going there and spending time with them. Their media, their "leaders" and their foreign policy more accurately reflect the interests of their powerful elites than the spirit or even the interests of the general population.