This chautauquan is long.  Lawrence of Arabia continued his time with the Arabian tribes. In conjunction with the allies they fought their way north to Damascus in Syria where an armistice with Turkey eventuated. 
Lawrence and Amir Faisal (son of Husseim of Mecca) and the Beduins fought onwards.  Australian soldiers, along with the rest fought. One tactic was to create trouble on the Railway line and lead enemy forces to defend it and leave other places vunerable.

An incident is recorded with Lawrence and the Australians.  Against expectations, Lawrence did not enter Damascus first at the time of the surrender.  An Australian War Memorial account explains that communications were unclear and Australian Light Horse went ahead before him.  Some say Lawrence was embitted by having been beaten and he downplayed the role of the Australians in the war.
Concessions to Arab nationality stipulated French colonial rule in Syria would be in the coastal regions.

Lawrence went with the Arab delegation to the Versailles Peace Confrence where they fully expected to be rewarded with independence for helping the Allies. Britain and France carved up the Middle East into their Zones of influence and the French even ejected Faisal from Damascus. (History Learning Site)
So WW1 ends. Do they have short memories in the Middle East or is that why troubles brew against the West?