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On September 25, 1939, Stalin suggested to German ambassador the exchange of Lithuania for areas near Lublin and east of Warsaw. (Weinberg, p. 59)
The secret protocol was signed to that effect on September 28.
The stated reason for the exchange was the public "explanation" of Soviet invasion, which tied it with protection of minorities (Ukrainians or Belorussians, the ethnicities prominently present in Soviet Union) and there were no such in the Lublin area or Warsaw area. (Marples, p. 108)
As a small side note, a bit of Lithuanian territory (Mariampol) was left in the German sphere of influence.
One of Wikipedia maps shows the territory exchanged for Lithuania (the dotted orange line)
Upvote:4
The basic problem that revision was solving was that the Germans by that time had invaded Poland, and had taken more territory than was allotted them in the original agreement.
They couldn't just give it to Russia. From the Russian point of view that would prove the two were working together, and from the German point of view, Hitler was not the kind of guy to be happy to give away hundreds of square miles of land his armies were already occupying.
Giving Stalin the last remaining Baltic State was the easiest solution.