It could develop as a teacher - student relationship. The Great Fairy Lemon could teach Link about the deeper magics of Hyrule. She might start with simple lessons, like how to better control his magical items. As Link progresses in his learning, he becomes more confident and starts to rely on her advice more. This creates a bond between them where Link looks up to her as a mentor, and the Great Fairy Lemon takes pride in his growth.
Their relationship could develop through mutual respect. Link respects the Great Fairy Lemon's power and wisdom, and she respects his courage and determination. For example, every time Link visits her for a power - up, they have a brief conversation that gradually deepens over time. They start to share stories about their experiences in Hyrule, which brings them closer.