Jewish lineage is not tied to DNA. A Jewish woman could marry a non Jewish man. Any sons would not have a Jewish Y chromosome, that son could marry a non Jewish woman. But the children could inherit the faith and culture and property rights of the original Jewish woman as well as tribal identity. Several studies have shown Jewish Semitic DNA in all Jewish communities in Europe, but not every individual. So, DNA test would not be conclusive, it would take a complete family history.