The Klaipėda Region, detached from the German Empire after the end of World War I and put under French administration, was not initially planned to be granted to Lithuania. The government of France and its governor in Klaipėda, Gabriel Jean Petisné, did not believe in the longevity of an independent Lithuania and saw it as an ephemereal state about to be incorporated into their primary Eastern ally, Poland.
From 1920 to 1923, the popularity of reorganizing the Klaipėda region into a Free State ("Freistaat Memelland") similar to Danzig grew among the population, both German and Lithuanian speaking - the Germans saw no desire to be incorporated into Lithuania, and that a Free State would be the first step towards rejoining Germany, while the Prussian Lithuanians feared that Klaipėda joining the republic of Lithuania would be not a "union", but "annexation", and their separate identity would falter in such a scenario. The Free State solution was endorsed by the French administration with Petisné at the helm and by 1923, the first foundations towards establishing a LoN-protected Free State were being laid.
The threat of Freistaat Memelland being formed was so large that Lithuania, with the secret support of the government of Germany (which, unlike the Germans in the Klaipėda Region, believed that a free state would be harder to retake than one which is held by a weak Lithuania), staged a rebellion in Klaipėda, mostly executed by Lithuanian soldiers out of uniform who infiltrated the region beforehand (which I guess makes this pretty ironic). Because France was dealing with the occupation of the Ruhr at the time, they couldn't defeat the uprising, and after a year of diplomatic crisis and discussions between Lithuania and the Entente, the region was handed to the Republic under autonomous status.
So, the alternate scenario is obvious. The Klaipėda Uprising is defeated one way or another, or its perpetrators are caught before it can take place, and the region is instead reformed into the Free State of Memelland.
Which would probably rejoin Germany even faster than the Saar, given that it, like Danzig, or even the autonomous Klaipėda Region of OTL, would likely see a NSDAP victory as early as 1933, but wouldn't have a strong nearby power like Poland preventing any incorporation of the region into Germany.
And Germany gaining full economic domination of Lithuania through controlling Nemunas and Klaipėda six years earlier and without the diplomatic conflict over Klaipėda between Germany and Lithuania would probably put Lithuania in the German sphere a lot faster and a lot more solidly.
Thoughts?