I've heard people arguing that Belarus is closer to how Lithuania used to be in times of the Grand Duchy and as a part of the Commonwealth. In one of his videos, Norman Davies also said that the official language of the Duchy was Ruthenian. What would then be the place of the predecessor to the Lithuanian language and culture as we know them today in the Duchy?
The somewhat glib answer to "real" cultural succession is a mixture of no one or it depends on how one interprets culture. Although the Commonwealth had a rich cultural legacy, fitting such early modern idioms into modern-day conceptions of national identity like Polish or Belorussian is a highly difficult task. "Ethnicity" in the in the Commonwealth was highly fluid and plastic concept and common twenty-first century markers of ethnic identity like language do not fit. For example, bilingualism complicates trying to lay specific claim on cultural figures of the Commonwealth. The Lublin Union began a process wherein Polish became the language of state and high culture in the Lithuanian regions, while the local vernacular remained intact and distinct from Polish. No one contemporary nation-state can convincingly lay claim to be the direct heir to the Commonwealth because nationality as a fundamental concept of identity did not exist in the early modern period. Is a poet who writes in Polish but self-identifies as a Lithuanian and comes from the Lithuanian gentry Polish or Lithuanian? There is no easy answer.
This problem has not prevented nationalist activists and some nation-states to try and derive legitimacy from the Commonwealth. Timothy Snyder's The Reconstruction of Nations: Poland, Ukraine, Lithuania, Belarus, 1569–1999 is a book that delves into both the Commonwealth and how the post-partition generations have tried to sublimate its cultural legacy into their national projects.