Poland did get a significant part of East Prussia, in fact the Warmian-Masurian Voivodeship which is made up from former German lands is around 1/3 larger than the Kalingrad Oblast. There were some plans to transfer the remainder to the Lithuanian SSR going back to 1944 however it only received Memelland which Lithuania had already captured after WW1 but was forced to cede it back to Germany in 1939.
While East Prussia was never a part of any Lithuanian state, it was perceived (and still is) to be culturally and historically important to Lithuania. e.g. the first Lithuanian book was published in Königsberg and most Lithuanian books published prior to 1905 were printed in East Prussia. Before the start of WW2 it still had a non insignificant Lithuanian speaking minority. Lithuanians likely made up the majority of the population in the north-eastern areas (called Lithuania Minor) until the plague of 1710, however by the 20th century most of have been mostly Germanized and even those who maintained their language weren’t very keen about joining the Lithuanian state established in 1918 due to cultural and religious differences and economical concerns (Lithuanians areas in the Russian empire were extremely underdeveloped compared to East Prussia).
Even in Memelland, which was probably one of the least Germanized areas of East Prussia, around half of the Lithuanian speakers identified themselves as Memellanders rather than Lithuanians. Memelland was the only part of Lithuania where free elections were still held after the coup of 1926 (because of an agreement signed between Lithuania and the Entente in 1924, which guaranteed various rights for the local population) and pro-Nazi German parties regularly received over 80% of the votes in the 1930’s despite only around half of the local people identifying as ethically German.
Anyway, I just wanted to give some context about the region, by 1944 the population question was largely irrelevant since almost all of the local Lithuanians were treated as Germans and most of them fled as the the German army was retreating or were expelled in the following couple of years (e.g. in 1945 less than 50 people out of the pre-war population of ~50,000 remained in the city of Memel itself). However some even in the Lithuanian communist party still considered that Lithuanian had a strong claim to the region and expected that more territory (besides Memelland) will be ceded.
I’m not aware of any official reasons of why that didn’t happen however we must take into account that the Soviet control of Lithuania was fair unstable in immediate aftermath of WW2. There was widespread armed resistance to the soviet occupation in the most areas outside of the major cities which lasted into the 1950’s (along with mass repressions and deportations). So the Soviet leadership probably wasn’t too eager to expand it’s territory at the time.
In addition to that local communist authorities in Lithuania didn’t really seem to want the area themselves. Lithuania lost a huge proportion of it’s population during the war and hardly had enough people to settle in the severely depopulated Memel and Vilnius (most of the population was Polish or Jewish prior to the war and most Poles were deported in the 40’s) regions which were assigned to the Lithuanian SSR. This meant that East Prussia would be mainly settled by ethnic Russians and the leadership of the communist party in Lithuania generally had a policy of resisting mass settlement of Russians in the republic (unlike in Latvia and Estonia local communist leadership wasn’t purged and ethnic Lithuanians made up most of the higher ranks in the party throughout the entire Soviet period). Later on during Kruschev’s thaw in 1961 there were some attempts to transfer parts of the region to Lithuania, but allegedly the first secretary of the Communist Party of Lithuania A. Sniečkus declined the offer supposedly due to similar concerns.
I have an older answer here, but as it is quite old, I'm happy to field any follow ups people may have about this, or clarify things.