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.
Her honesty could be one. If Lizzy is always truthful, it makes her trustworthy and appealing. For instance, she might always give honest opinions about things, which the speaker values.
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.