Q. 1. My sister who is a Catholic, she being married to a Lutheran in the Catholic Church, was told that she does not qualify to be the Godmother of my child. Can you explain why?
A. 1. As you indicated, your sister is involved in a mix-marriage. In many cases, persons who are involved in a mix-marriage, they believe that their children should choose their own religion when they grow up. Such a belief disqualifies the candidates as potential godparents in the Catholic Church. I suspect that your sister must have been interviewed by the parish priest who concluded that her aforementioned belief disqualified her as a Godmother.
Those who wish to be Godparents, they must preach and defend the Catholic faith, such being the commission they received from their Bishop when they received the Sacrament of Confirmation.
I recommend that you find a candidate who is in good standing with the Catholic Church. That means one who believes in all the teachings of the Catholic Church, without exception, one who practices the faith, one who will be a good spiritual mentor to your child.