The British are humiliated when none of the borders stand for long, Turkey probably joins the Axis in WWII thereby destroying the British Empire, relations with France are ruined for this treachery...
Not many, certainly not enough to form a nation from. The only way this would have been feasible is to expel all Turks from the area and snatch every Armenian from Armenia proper and force them to settle in Lawrence's Armenia state.
Seriously Lawrence of Arabia must have been high on gas fumes when he drew up this map.