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I believe the imposter is supposed to have been installed at the time Sr. Lucy was "transferred" to a different convent. I forget what year that happened, but the evidence points to that being the time the switch was made.
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That makes sense, because it would be by far the easiest way to switch her out. You can't exactly get a bunch of cloistered nuns to pretend that some new person who showed up in the convent is Sr. Lucy, and not ask questions as to what happened to the real Sr. Lucy. The cleanest way would be to tell the nuns at one convent that Sr. Lucy is leaving, transfer her out, and send the imposter to the new convent. Since the nuns at the new convent don't know Sr. Lucy personally, they would have no way to know the new nun who showed up is not her.
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As far as what happens to the real Sr. Lucy, once she is out of the convent, she can be "disposed of", to borrow a term from mafia movies.
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That is similar to what happened to Bp. Thuc. A group of modernist monks told them they were going to take him to see some people, I forget who, and once they got him in the car they headed straight back to their monastery and held him incommunicado until his death, which (by a strange, aherm, coincidence), was only a few months later.
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The ramifications of this are interesting, too, in that it would mean that the famous Fr. Fuentes interview was with the imposter. That was when Sr. Lucy supposed made prophecies about the future of the United States and also of Russia.

Good post, but, depending on what you mean by your last sentence, the real Sr. Lucy met with Wm. Thomas Walsh in the 1940s, and she told him about the whole world being communist, including the USA, in that interview.  That interview was ~1946, and she was supposed to have joined the Carmelites a few years later.  

Sister Lucia of Fatima in 1946 said that the whole world would become communist
 
While he was the pastor of Our Lady of Fatima Church in Ludlow, Massachusetts, I spent some time with Fr. Manuel Rocha, the interpreter selected for Mr. William Thomas Walsh, who wrote perhaps the most popular book on Fatima. Fr. Rocha told me that one of the questions Mr. Walsh asked him to translate to Sister Lucia during a three hour interview on the afternoon of July 15, 1946, while she was still Sister Maria das Dores, a Dorothean Sister at Vilar near Porto, Portugal, was asked; In your opinion, will every country, without exception, be overcome by communism? Her pale brown eyes staring into his, a little dimple on each cheek, she answered, Yes. Fr. Rocha related to me that Mr. Walsh wanted to be positive about the answer and therefore repeated the question adding, And does that mean the United States of America too?  Sister Lucia answered, Yes.