The Mandates were assigned to the successor states. Check your timeline. The British Mandate for Palestine did not start until 3 months after the signing of the Treaty of Lausanne.Except none of the states were states. Syria wasn't a state. Lebanon wasn't a state. Jordan wasn't a state. Iraq wasn't a state. And "Palestine" (now Israel) wasn't a state.
They were territories under British stewardship. If they were states there would have been no need for the stewardship nor the Mandates. The Mandate indicated that a necessary transition had to occur before independence and recognition.
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Drawing up the framework of nationality, Article 30 of the Treaty of Lausanne stated:
“Turkish subjects habitually resident in territory which in accordance with the provisions of the present Treaty is detached from Turkey will become ipso facto, in the conditions laid down by the local law, nationals of the State to which such territory is transferred.”
The Mandates were to hold those territories in trust and to help them to create the institutions required to achieve independence.
Not a single mention of "Pal'istan".
Are you not aware that the Treaty of Lausanne was as end to hostilities and had nothing to do with your invented "country of Pal'istan"?