Since this is doable in a multitude of ways let's make it a bit more challenging. So POD in 1923, the Lausagne negotiations break down and the Greeks attack in East Thrace. At the moment they had numerical superiority of roughly 3-4 to 1 on the armistice line, the Greek navy could probably hinder shipment of reinforcements from Anatolia and the western allies were mildly supportive. Greek army ends up on the Bosporus but unable to attack the Turkish army in Anatolia, Turkish army cannot cross the straits either with Greek battleships and 9 divisions behind them and peace is signed on the status qwo.
Turkey is pissd off enough to be somewhat more pro-axis during ww2 but not enough to make the mistake of jumping in, while Ismet got discredited enough for the more autocratic Recep Peker to succeed Kemal. On the other side of the straits Greece was somewhat more stable and more solidly Venizelist .It enters the war as a republic in 1940 and avoids civil war afterwards, the government in exile in Crete has no legitimacy issues unlike OTL. Come 1949 Greece joins NATO but Turkey does not although it still receives military and economic aid. Come to 1950s-60s union of Cyprus with Greece follows more or less peacefully and with US support...