The name Lucy (or the variant, Lucie) is mentioned by Paul, John and replacement John [the man who replaced John Lennon beginning in 1966] from 1965-on:
1965: On the tape that had Paul's Christmas gift recording for the other Beatles (called Unforgettable), John recorded over it with a reading from children's author Beatrix Potter's book, The Tale of Mrs. Tigglywinkle which is about a little girl named Lucie who loses handkerchiefs and a pinafore and goes looking for them. (A passage from the book): "Lucie climbed upon the stile [a set of steps for passing over a fence or wall] and looked up the hill behind Little-town - a hill that goes up-up into the clouds as though it has no top!"
1966: Paul's quote from John Micheline's short story, "In the Bronx": "Lucy had no panties on." [Mispelled as "Lucie" in the article.] The boy in the short story goes to a playground and finds Lucy swinging on a swing. The air pushes her dress aside and she has no underwear underneath. He describes her as a wild girl. The boy takes her to a park and kisses her. She pulls away from him and tells him she will tell her boyfriend that the boy raped her. The next day, the boyfriend finds the boy and beats him up.
1967: Replacement John's Lucy in the Sky with Diamonds about someone on an LSD trip and a girl named Lucy who appears and disappears throughout the experience.
1973: Replacement John's Bring on the Lucie (Freda People) which was supposed to be an anti-war song but has more personally-directed lyrics like:
[spoken word intro]: Alright boys, over the hill! . . .
We don't care what flag you're waving;
We don't even want to know your name.
We don't care where you're from or where you're going;
All we know is that you came.
You're making all our decisions . . . [This passage suggests that the B/Featles were not fully aware of who was behind the things happening to them; akin to Faul's Maybe I'm Amazed's lyric: "Maybe I'm a man, maybe I'm a lonely man who's in the middle of something that he doesn't really understand."]
Well, we were caught with our hands in the air . . .
We understand your paranoia,
But we don't want to play your game.
It's difficult to speculate how all the references connect, but it appears that Paul met a girl--or thought he did when he was in a hallucinatory state--possibly in a park--and something happened between them. An incident--or virtual incident--that could have been used against Paul.