Up until now, such permits have not been issued for the reason that Lithuania does not recognize same-sex marriages.
ECHR ruled in June that the same-sex partners of EU citizens have the right to reside in any EU member states, even if it does not recognize same-sex marriages.
"Now, if wee need to make a decision based on the existing jurisprudence, the decision would be to issue a residential permit," Evelina Gudzinskaitė, director of the Lithuanian Migration Department, told journalists on Thursday.
Earlier, Lithuanian institutions were of a position that foreigners who wished to receive a residential permit on the basis of family reunion had to register in Lithuania the marriage they entered into abroad.
On Tuesday, Lithuania's Constitutional Court is due to start hearing the case of a Lithuanian citizen who entered into same-sex marriage with a Belarusian in Denmark but the Belarusian was later refused a residence permit in Lithuania three years ago. The Court will look into whether the Constitution was not breached in this case.