Is a fake Sr. Lucy a mere conspiracy theory?

You have seriously misstated things here. Our “doctrine” doesn’t hinge upon Sr. Lucy of Fatima or any other individual. 

Galatians 1:8-9 “But though we, or an angel from heaven, preach a gospel to you besides that which we have preached to you, let him be anathema. As we said before, so now I say again: If anyone preach to you a gospel, besides that which you have received, let him be anathema.”

The fact that the Vatican II sect is not the Catholic Church is a provable fact from many dogmatic teachings and the undeniable heresies and false doctrines which the Vatican II sect teaches. It’s insulting to the importance and the authority of these dogmas, as well as the significance of the heresies of the Vatican II sect, to describe things the way you have. One could argue that for Fatima to make sense to those who hold our positions it would make sense that there was a false Sr. Lucy, I would agree. But that would also be true of all who reject the Vatican’s version of the Third Secret, and hold that John Paul II didn’t sufficiently consecrate Russia – which includes about 100% of traditionally-minded professing Catholics. They would all have to agree with us that the post-Vatican II Sr. Lucy was a fraud, if Fatima is to make sense to their position (a position which rejects the post-Vatican II Sr. Lucy’s testimony that the Third Secret was revealed and that Russia was consecrated successfully by John Paul II, etc.) Further, it’s not a mere conspiracy theory that there was a fake Sr. Lucy. There is photographic evidence and undeniable evidence from the false Lucy’s testimony on matters pertaining to Fatima. This testimony proves she couldn’t have been the real one.