I think you get things like a much nastier German civil war. Realistically, they either have to win big in war (say all Germans become this new religion and are so strong that the Catholics and to lesser extent Orthodox can't threaten them or they are slaughter in holy war or they are expelled to other parts of the world if late enough colonies exist. Heretics are always treated worst than people who are simply of other fates. So it is either a case of genocide or a Lutherian wank, and a big wank.
So how big a wank does it take. It means for example that the Hapsburg (Spanish) and French and Italians can't do anything about it. Since we are talking a region of Germany that starts Lutherianism, we could need all Germans (say all of HRE, Dutch, Swiss, all Germanic peoples plus few others) to immediately convert and unite under Lutheranism to strong state. Then win the great war. It would have a brutality level that we associate with the Nazi, IMO. Ugly TL, but if you can write the POD, it is plausible.
And if we look at Mormonism, which to me deserves separate religion status of Abramhamic religions along with things like Druze and Alawite, the I think we can get some ideas of what happens. Lutheranism will pick up some elements from other religious traditions to justify the new prophecy. In this case, it is from the pre-Christian German traditions which I can't really give any real good details of what would even be likely.