Sodano was also a key player. So maybe it should be Gang of 5. Then, more recently, you could add Bertone. But "Gang of Four" sounds better because the term was previously used of the early Chinese Communist leaders.
But all this pertains to the coverup of the Third Secret, not necessarily to the disappearance of Sister Lucy.
While it's theoretically possible that she died of natural causes, and they needed an imposter for something, I find it more likely that she was taken out. Sister Lucy knew the contents of the Third Secret and would have been able to apply it to V2, the NOM, and the papal imposters.
From the Dimond Brothers:
Whenever that may have occurred, there is no doubt that the woman playing the part of “Sr. Lucy” since Vatican II was not the real one. Readers can take this for what it is worth (and it is not essential in any way to the facts above which prove that there was indeed an impostor Sr. Lucy), but a few years back we received a very disturbing letter. We received a letter from a woman (a traditional Catholic convert) whose family was involved in the higher-echelons of the Illuminati and Fɾҽҽmαsσɳɾყ. We also spoke to this woman both before and after she sent it. There was much more in the letter and in the telephone conversations that added context and creditability to her claim, but we can only give a portion of the letter below. As hard as this may be to believe, we really did receive the following letter and speak at length with this woman (she asked that we withhold her name for obvious reasons):
“Dear Brothers of Holy Family Monastery… As I told you on the phone I have some very dark relatives…[a world famous Freemason] is the brother of [x- name removed to preserve anonymity of author] who was married to my Grand Aunt. All of my relatives on my mother’s side were 33rd degree Illuminati Freemasons. My Grandparents were in Eastern Star… I know I must sound like a screaming weirdo by now. I am not… When I was five my Mother hosted a gathering. There are many things that went on that are too gruesome to put in print about these gatherings. They are basically sacrificing to satan to put it briefly. I had a new baby brother named - … My mother didn’t know ahead of time [that x] was to be part of the ‘ceremonies’. They were going to put him in what looked like a large brass wok [and torture him] in order to tell the future. …[thankfully, this didn’t happen because of intervening events]… [But] One of the things that was said that awful day was they had just killed sister Lucy (I thought they were talking about a sister I didn’t know I had that they had killed). When I asked they said ‘No stupid…she’s a nun’ It only made sense years later what this meant. It was 1958, late Oct when this happened. [I remember because my brother had just been born]. I know that I sound like a mad woman but it is the truth…”
Of course, late October 1958 was shortly after the "election" of Roncalli.