Is a girl who lied about the existence of a needy woman requiring rent money for her home in order to receive donations for herself, and was given money on that basis, obligated to do anything in this situation?

It is not permissible to dispose of money collected to help a woman pay her house rent for one's own benefit without the donor's permission. It is advisable to seek Allah's help and supplicate to Him, and to inform the donor that the matter is incorrect, then seek her permission to spend the money on those in need. If she agrees, then there is no harm in spending it to fulfill one's own needs if the person is in need.