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.
Another option is to plan a special date. Take her to a place that has significance in your relationship, like where you first met. During the date, be honest and tell her how you feel. You can also give her a small gift that represents your feelings.