The old Grand Duchy of Lithuania was very much what we would today call a multi-ethnic state, insofar as today's vocabulary can be applied to the period before the emergence of modern nationalism. Vilnius was the capital of the state called Lithuania, but in the early 20th century ethnic Lithuanians had minimal presence there. The Russian, German and Polish censuses pre-WWII all record a negligible number of ethnic Lithuanians, circa 2%. Upon the occupation of the city in 1939 Lithuania began settling ethnic Lithuanians there which probably accounts for the increase recorded by the Germans in the 1940s. But prior to that the number of ethnic Lithuanians was negligible. Post-WWI Lithuania re-emerged as a nation-state which sought to suppress minorities within its territory, and not a continuation of the old multi-ethnic Lithuania. So it could hardly pose as a continuation of a state of a different type.Why anachronistic though? I'm not denying that it was majority Pole and Jewish at the time, but it's not like the Lithuanian population was nonexistent. Every demographic census in that region from 1897 to 1942 (I'm excluding the Soviet census since many poles were transferred to Poland) was very different depending on who did it (Russians, Germans, or Poles) and I'm not counting the Lithuanian censuses for obvious reasons. So we could say that at least 15-20% of Lithuanians were living in that region (not the city) or maybe even more. And in history, many nations had claims for regions that didn't have that many percent. Besides that, it is the historical capital.
I would say that Lithuania had the same claim as Poland did.
Being an ethnic Lithuanian state, and claiming the ethnically very much non-Lithuanian Vilna/Wilno/Vilnius area, was like wanting to have one's cake and eat it too.
States at the time found all sorts of reasons why they deserve more than the areas where they made up most of the population but I can't think of another case where a state wanted to stick it's capital in a city and area where its ethnicity was virtually absent.