Even though you never had a Lithuanian nationality (citizenship) you may “restore” it if at least a single parent, grandparent or great grandparent had it. In this case, the usual requirements for naturalization (10 years residence in Lithuania, speaking good Lithuanian) will not be applicable.
To restore nationality one has to provide documents proving that his/her forefathers had a Lithuanian nationality and that he/she is their descendant. The forefathers‘ nationality could be proved with a passport, army service documents, state service documents, personal certificate. If there are no such documents you may provide other ones (e.g. ones proving a place of residence). There are possibilities to look for historical and genealogical data in Lithuanian State Archive.
Simplified nationality for Lithuanian diaspora
Even if your forefathers never were Lithuanian nationals or you may not prove it you may still have a route to simplified Lithuanian nationality if you are a Lithuanian. This system works for ethnic Lithuanians from the historical Lithuanian communities that were left outside modern-day Lithuania as well as descendants of pre-1918 migrants (i.e. those who emigrated before modern Lithuania was established). In order to become Lithuanian national this simplified way it is also not necessary to live in Lithuania.
Right to nationality certificates
If you seek to acquire Lithuanian nationality later (because, for example, you are not yet willing to denounce your current nationality) you may now apply for a Right to Nationality Certificate. The certificate is issued to members of Lithuanian diaspora after they prove their right to Lithuanian nationality as specified above. When you‘ll finally decide to become a Lithuanian national you will not need to prove it all again. “Right to Nationality” also gives you a right to easily get a residence permit in Lithuania (despite not being a Lithuanian national).
Technically there are two types of these certificates (one for proving a right to restore nationality and one for certifying Lithuanian descent), but they are nearly identical in their meaning.
Dual nationality in Lithuania
According to a controversial decision by the Constitutional Court of Lithuania dual nationality is only permitted in Lithuania in rare circumstances. Under the 2016 Law on Nationality such “rare circumstances” have been greatly expanded however: they include all the Lithuanian citizens who were expelled from Lithuania or left the country before 1990 03 11 and their descendants (up to great grandchildren), except for those who left willingly to Soviet Union. If you are not among those eligible for dual citizenship then you‘ll have to renounce your current nationality after gaining Lithuanian one.
History of the Nationality Law shows that these norms have been changed especially frequently (e.g. before 2006 Constitutional Court decision special circumstances for dual nationality encompassed everybody who did not repatriate). In the future, the right to dual nationality may thus be further limited. Dual nationality (under normal circumstances) is prohibited by the 1st part of the Constitution which means this could be changed by referendum alone and the Referendum procedure in Lithuania is one of the toughest among democratic countries, largely rendering the referendums on constitutional change impossible to succeed (even if the majority would support wider application of dual nationality). Therefore if one could get a dual nationality under a current law perhaps he/she should hasten to seek it.
Dual nationality is controversial in Lithuania for a couple of reasons. On the one hand, Lithuania seeks to foster a connection with a million-strong Lithuanian diaspora to prevent their complete assimilation and have them as a support for the “dying out and emigrating” Lithuania. On the other hand, there is a fear of a situation such as happened in 2008 Georgia where Russia issued its own nationality to thousands of people from local ethnic minorities and then, due to disagreements with Georgian policy, invaded the country justifying it by the “protection of Russian nationals”.