Lizzy might be a person who has had a significant impact on the author's life. She could be a neighbor who was always there to help, and over time, the narrator developed deeper feelings for her. It's also possible that she's someone the author met during a trip, and they had a special connection from the start.
Hard to say for sure. Sometimes authors draw from real-life events, but they might also purely invent the story. Without more background info, it's tough to tell if 'I Love Lizzy' has a real basis.
I'm not sure specifically which 'I love Lizzy' true story you're referring to. It could be a personal story of someone's love for a girl named Lizzy, perhaps a story of friendship turning into love, or it could be a unique experience that only the people involved really know the details of.