Both Lithuania and part of Poland were occupied by Russia from 1795-1918. Neither existed as independent nations.
Russia divided current day Lithuania into 4 gubernias (Russian for province). The four were Vilnius/Vilna/Wilno, Kaunas/Kovno, Suvalkija/Suwalki, and Gardinas/Grodno.
The Suvalkija/Suwalki was one of the 10 provinces/gubernias that comprised the "Kingdom of Poland" that was headed by the Russian czar so it really wasn't an independent nation state. The "Kingdom of Poland" was also called Russia Poland.
My mother's parents were both from Suvalkija so Ellis Island recorded them as Russian citizens (which they were) whose ethnicity was Lithuanian. They came from the northern half of the gubernia which is present day Lithuania. The southern half (including the provincial capital of Suwalki/Suvalkija) is in Poland.
Your best bet would be to find the church in the UK where they were married and see if the church marriage register lists where the bride and groom were baptized and the names of their parents.
If they were married in Lithuania before emigrating, you wouldn't have that source of information. However, if they had siblings who emigrated to the UK, perhaps their church marriage records would have that information for you.