APOSTILLE
If you wish to prove the authenticity of a document issued in Hungary in order to use it in Lithuania, Apostille authentication is required.
For Hungarian documents, the Apostille certificate is issued by the competent Hungarian authority (Ministry of Foreign Affairs and Trade, Ministry of Justice, Hungarian National Chamber of Notaries) in Hungary.
Consulates or embassies are not competent in issuing Apostille certificates (nor is the Embassy of Hungary in Vilnius). You can read more about the Apostille certificate here
In order to use a Lithuanian document in Hungary, the competent Lithuanian authority issues an Apostille (the Embassy of Hungary in Vilnius is not competent).