Lithuania has more historic ties with Belarus. Belarus and Lithuania were in the same political state known as the Grand Duchy of Lithuania since 1250.  In 1569 Polish-Lithuanian commonwealth was formed with core Grand Duchy of Lithuania was what’s today Lithuania and Belarus. In 1795 Lithuania and Belarus were incorporated into Russia. Poland had an autonomy, while Belarus and Lithuania were known as north-western kraj. In 1918 new independent states appeared largely based on ethnic identities and languages spoken.

Only eastern Latvia (Latgale) is more russified than Lithuania.

PS The region of your ancestry – around Grodno – was historically known as Litva (Lithuania) until at least mid 19th century. It does not mean Baltic speaking people were living in that region