Hi Sharon, the parent project is Slavic Roots and this incorportes countries that are predominantly or partially of Slavic language, ethnicity, and heritage including: the Czech Republic, Ukraine, Slovakia, Bulgria, Belorussia, Slovenia, Bosnia, Croatia, Russia, Serbia, and Poland.
While not Slavic per se, the Baltic States (Lithunia, Latvia, and Estonia) have large Russian minority populations as does Kazakhstan. As these countries were part of the Soviet Union, membership to the Slavic Roots Project would be warranted and may be useful.
From 1795-1918, Lithuania was indeed a Grand-Duchy, but part of the Russian Empire. I would think you should apply to the Russia Project.
To note: membership in any of the sub-projects automatically enters you in the Slavic Roots project as the badge is the same for all: