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.
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.
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.