Landsbergis discussed the issue with Belarusian opposition leader Svetlana Tikhanovskaya last Friday.
Lithuanians now call the neighboring country "Baltarusija", which translates as "White Russia".
"The name by which call our neighboring country should not entrench the (Soviet-era) understanding of Belarus as part of Russia," Landsbergis told BNS.
"Belarus means White Rus', not Russia, and that must be reflected in the name we use," he said. "If Belarusians express such a wish, we'll certainly consider this issue, just as we have already changed the name of Georgia to Sakartvelo."
The State Commission of the Lithuanian Language has recently approved "Sakartvelas" (Sakartvelo) as the official name for Georgia, meaning that it has to be used in all official Lithuanian-language documents.