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If you are a third country national, residing in Lithuania based on a residence permit „Leidimas nuolat gyventi - Ilgalaikis gyventojas – EB“ and you intend to move to Germany permanently, you are allowed to apply for your German residence permit directly in Germany after you moved there (Art. 38a German Aliens Law). Be aware that this rule does not apply for short term stays and stays in connection with providing services or seasonal employment. You have to apply for the residence permit within 90 days after entering Germany. If you fail to do so, you have to leave Germany and apply for a visa in your home country.
Be aware as well, that you are allowed to work only after you have received the German residence permit including work permit. If you intend to work directly after entering Germany, you should apply for a visa at the embassy in Vilnius. Information on how to apply for a visa can be found here.
The embassy highly recommends to contact the aliens‘ authority at your German place of residence for further information before moving to Germany.