There are several reasons she cannot receive in the Catholic Church, the Eucharist is part of that. Their understanding of the ‘real presence’ DOES differ from Catholic understanding. I cannot explain the complexities but I do believe Lutheran’s believe in consubstantiation which is not compatible with Catholic belief (basically they believe that while the bread becomes Christ it ALSO remains bread… and thus is not sacred, since it’s really just bread. Something like that, I don’t explain it well).
Furthermore, when you receive communion in ANY Church you are also professing your belief in that Church!!! As a Protestant I was always taught that to partake of communion is to show your outward support of that particular church. If she were to go up and receive communion in the Catholic Church all who saw her would presume she is Catholic! And that she believes all that the Church teaches! Does she really want people thinking that? Does she want to make a public statement that she believes all the Catholic Church teaches???
But last and foremost, she should not receive because the Church asks her not to (all non-Catholics are asked not to receive expect, perhaps, the Orthodox (in dire circumstances)), and it would be the ultimate in disrespect for her to receive anyway. Why would she want to disrespect the Church she also wants to take communion from? That makes no sense. Respect demands that she not receive so long as she is not a confirmed, baptized Catholic.
I would NEVER go to a Muslim country and demand that I be allowed to pray with the men. Nor would I go to a Buddhist temple that has made a vow of silence and walk around talking at the top of my voice. Why? Because we should respect other religions, even if we don’t agree with them.