According to information available to BNS, the decision was taken on Wednesday after hearing of the plea filed by the Kurdish family from Iraq.
Under the decision taken by the Migration Department last October, the Kurdish group had to be sent back to Iraq without getting an asylum, a refugee status or additional protection.
Sources told BNS that court's ruling was based on the fact that the migration authorities failed to abide by procedures for objective assessment of all circumstances.
The Kurdish family had been relocated to Lithuania from Greece.
Under the European Union (EU) quota, Lithuania has committed itself to receiving 1,105 refugees by this September. Lithuania has already resettled 254 asylum-seekers, including 229 from Greece and 25 from Turkey. Some 142 of them have already left Lithuania for other EU countries.