"I prefer to have my cousin as a sponsor for my child in the Catholic Church. She is a practicing Lutheran and is a deeply Christian woman. I am a Roman Catholic. Before I ask her, I would like to know if this is permissible?"

This is not permissible in the Catholic Church. To be a sponsor in a Catholic baptismal celebration, the Church requires that the person who agrees to be the sponsor must 1) be properly designated to  be the sponsor; 2) have completed the sixteenth year of age, unless another age has been established by the diocesan bishop, or it seems to the pastor or minister of baptism that it is justified to make an exception for a just cause; 3) be a Catholic who has been confirmed and received the Sacrament of the Eucharist and lives a life in harmony with the Faith and the role to be undertaken as a baptismal sponsor; 4) is not bound by any canonical penalty; and 5) is not the father or mother of the one to be baptized (Code of Canon Law, Can. 874). This same Code says that a non-Catholic is not to be admitted as a sponsor. The Church requires at least one sponsor at Baptism, and this sponsor must be Catholic. A non-Catholic can be a witness. Even if your cousin is an exemplary Lutheran and is deeply spiritual, she cannot give guidance to the child in specifically Catholic ways. She can serve as a witness to the child’s baptism and later be a good example for the child along with a Catholic sponsor.