Sr. Lucia said nor wrote anything about ‘three more popes’. (I have read most of the documents on Fatima.) And entire books on Garabandal, including Conchita’s diary are also online. The ‘three more popes and then it will be the end of times but not the end of the world’ is definitely a true statement from and associated with Garabandal (not Fatima). The statement is known to have been attributed to Our Lady by Conchita; the only question remaining is that of its interpretation - for even Conchita said she did not understand what it meant. (Most visionaries from various apparitions admit to being given messages, but not the interpretation of the messages, so it is not surprising that Conchita, like the rest of us, is left to wonder about its meaning.)
I 'll tell you the green book as it was known is still well worth reading about Fatima; “Fatima Journey” I believe is the title, no matter how much you’ve read on Fatima I’m sure you won’t be able to put it down, and it is I’m sure still the authoritative source on the subject. Fr. DiMarchi was given extensive interviewing priveledges with Sr. Lucia as he was the artist who sculpted the first statues of Our Lady of Fatima, based on the descriptions that she provided.
Back to our subject, where has the prediction about only three more Popes originated? Sr. Lucia in later years also wrote memoirs, alot of what she wrote reflected her disgust at the failure of the church authorities to act on the Fatima message, the consecration of Russia and so forth. She was a Mystic and I think she had another apparition many years later that prompted her to write letters to the Pope and some Bishops; it may be in this second apparition that this warning of only three more Popes, seems maybe to have begun, I don’t know.
I do know that I have heard of this prophecy since an early age, but I really never even heard of Garabandal or Conchita until the 1990’s. There seems also to be a possible connection in this to another prophecy that is widely known of, but that no one seems to know where it started from, and that is The Great Apostasy prediction.
Actually, again I’m with you I know where you are coming from, I come from there too, it’s a place where we know in our hearts more than in our minds that something is true that we believe in, no matter what the doubters might say. God bless you too