There is a very clear winner here, but I'm not entirely sure that it satisfied my geographical criteria. It is the book most frequently tagged "Lithuania" on both LibraryThing and Goodreads, and is by a considerable margin the most widely owned of such books. But as far as I can tell, most of the story actually happens on Russian territory; it is the story of a teenager deported to Siberia with her family after the Russian conquest of Lithuania in 1941. Published only in 2011 - but clearly already a best-seller - it is:
Between Shades of Gray, by Ruta Sepetys
The top books actually and clearly set in Lithuania by ownership on LibraryThing and Goodreads are both twnetieh-century classics, but score completely differently on the two systems. High on LT, low on GR, is a Nobel Laureat's story of growing up in a rural environment in which he and his family spoke Polish but almost everyone around them spoke Lithuanian. It's generally agreed that the setting is Šeteniai in Lithuania. Published in 1955. the book is:
The Issa Valley / Dolina Issy, by Czesław Miłosz
On Goodreads, by quite a long way, the top book set in Lithuania is a classic of Lithuanian literature, first published in 1933. It is the story of a priest who struggles with the contradictions between faith and art, and the ultimate victory of the latter. I'm surprised by how well it does on GR - perhaps it is a set text somewhere (it is amolst certainly a set text in Lithuanian schools). It is:
In the Shadow of the Altars / Altorių šešėly, by Vincas Mykolaitis-Putinas
Any more suggestions? We did well with the Georgia discussion.