You are right. the Ottoman Empire would have collapsed with or without Lawrence. Once the Greeks left the Empire was doomed.
Yes, the Empire was already in decline by the time the Greeks gained their independence. The power of the Sultans had been reduced to a joke... the old conquerors had been replaced by flabby and half insane rulers, and the empire was in truth run by the Janissary corps, until they were decimated under the orders of Sultan Mehmet II.
By then, it was too late to resucitate the empire. It was a long downward spiral.
There are some very very interesting archives of Enver Pashas diary as a military commnader in Bulgaria, and his despair at putting down Bulgarian uprisings.
Indeed, he notes a feeling og disgust at the policies of his own empire, suppressing the freedom of the Bulgarians, and expresses his displeasure at being the instrument of the destruction of their legitimate aspirations.
This apparently had some role in his later revolutionary ideas as a member of the 'young turks'.