One way is through detailed descriptions of their first encounter. For example, describe how Natsu's eyes lingered on Lucy, noticing every little detail like the way her hair caught the light. And for Lucy, how she felt a flutter in her stomach when she saw Natsu. Another way is to show their growing closeness through shared experiences. Such as when they have to rely on each other during a dangerous mission. This can build on that initial love at first sight feeling.
In a fanfiction, the concept of Natsu and Lucy's love at first sight can be developed by adding emotional depth. When they first see each other, not only should there be physical attraction but also an instant emotional connection. This can be shown through their dialogue. For instance, Natsu might say something that makes Lucy feel truly seen for the first time. Then, as they get to know each other better, the love at first sight can be contrasted with their new understanding. Maybe they realize that the initial attraction was just the tip of the iceberg, and there is so much more to their relationship waiting to be explored.
To develop their love at first sight in a fanfiction, start with their first meeting. Maybe Natsu is the first to approach Lucy, and his words are a bit clumsy but endearing. Lucy responds with her own charm. Then, as the story progresses, have them constantly thinking about each other. When Natsu is on a solo mission, he still has Lucy in his mind, and the same for Lucy. This shows that the love at first sight wasn't just a momentary thing but the start of something deeper. Also, have other characters notice the special connection between them, which can further emphasize their relationship.