What is the lineage of a girl born from an illicit relationship between a Muslim man and a Christian woman, who then married later before her birth? What is her religion, and does she need to renew her Islam if she was not attributed to her father?

This girl is a Muslim, and there is no need for her to renew her Islam. Her lineage has no bearing on that, as long as she embraced Islam after reaching puberty, for the Prophet, peace and blessings be upon him, said: "Whoever prays our prayer, faces our Qibla, and eats our slaughtered animal, that is the Muslim for whom Allah's protection and His Messenger's protection are guaranteed, so do not betray Allah in His protection." This girl is lawfully and correctly attributed to her mother and her mother's family, by which mahramiyyah (being an unmarriageable kin) and حرمة (sacredness) are established. She is not attributed to her father from zina (unlawful sexual intercourse).