Lindórië was the sister of Eärendur of Andúnië in Númenor. Lindórië was part of the tradition of the Faithful associated with the Lords of Andúnië, and she passed this tradition on to her daughter Inzilbêth. Inzilbêth became Queen to King Ar-Gimilzôr, one of the greatest enemies of the Faithful, but her elder son Inziladûn was of like mind with his mother. So, when Lindórië's grandson took the Sceptre of Númenor, he took an Elvish name, Tar-Palantir, and did what little he could to reverse the work of the King's Men.
Though we know the names of Lindórië's brother Eärendur, and daughter Inzilbêth, the name of her husband is harder to discover with certainty. A brief hint in Unfinished Tales suggests that his name may have been Gimilzagar, but (as Christopher Tolkien observes) Gimilzagar was the younger son of Tar-Calmacil, who lived at least three generations earlier, so this identity seems doubtful.