I heard somewhere that Stalin offered Kaliningrad oblast to Lithuanians but they rejected the offer. Also, not well known fact but for very, very short time there were Polish military control over city itself in 1944 or 1945, but I don't remember details.
The former may well have happened but it doesn't really matter, since its not like the Lithuanian SSR were ever truly independent to make a decision like that; especially when Stalin was still alive. Also any Polish control would have been the Soviet-backed Polish forces rather than the Home Army, which weren't very active in that area.