What should a girl do who lied to a young man, claiming to belong to a well-known family, and now wishes to atone for her sin?

Corresponding with a non-mahram man, lying, and claiming ancestry from a tribe to which one does not belong are all reprehensible acts that necessitate repentance. Such actions are not permissible even if one intends to achieve a worldly benefit through them. Repentance is obligatory for these acts. Nothing else is required of you, as long as you did not mention a specific woman by name.