They can develop their relationship by having small, everyday moments. For example, sharing breakfast together as a family, where they talk about their plans for the day. Natsu could show his love for Lucy by being more protective of her and their family in dangerous situations. Also, they could have inside jokes that only their family understands, which would strengthen their bond.
As they travel, their bond deepens. They start to rely on each other more. Natsu becomes more protective of Lucy, and Lucy begins to understand Natsu's impulsive nature better.
She might start to blush furiously. Given her character, she is a bit shy when it comes to romantic matters. And then she might start to stammer out a response, not really sure what to say at first. As she composes herself, she could tell Natsu that she has feelings for him too but in a very gentle and sincere way.
Well, Natsu is a passionate character. He could react with a lot of excitement. He might pick Lucy up and spin her around, laughing and saying how amazing this is. Or, he could also get a bit worried and start asking Lucy all sorts of questions about her health and what they need to do next.
Well, in some fanfictions, it could be through a dangerous situation. Maybe Lucy is in peril and Natsu's intense fear of losing her makes him realize his love. For example, if she's captured by a powerful enemy, Natsu's desperation to save her and the way his heart races at the thought of her being hurt could be the trigger.
Lucy might be heartbroken. After all, Team Natsu was like a family to her. She could initially go into a state of shock and disbelief. Maybe she would try to plead with the team to let her back in, explaining that whatever they thought she did was a misunderstanding.
One character that would be interesting to include is Mirajane. She has a motherly and observant nature. She could be the one to nudge Natsu and Lucy in the right direction when it comes to their relationship. For instance, she might arrange for them to go on a mission together that she knows will bring them closer. Laxus could also be in the fanfiction. His powerful presence can create a sense of danger or protection. If there's an outside threat to the guild while Natsu and Lucy are exploring their relationship, Laxus could be at the forefront of defending the guild, which would impact Natsu and Lucy's situation. And don't forget about Cana. She could be the one to create some light - hearted chaos, like daring Natsu and Lucy to do something that ends up bringing them closer, such as a bet that leads to a shared adventure.
In many fanfictions, Natsu protects Lucy by using his powerful fire magic against their enemies. For example, if they encounter a dark guild attacking Lucy, Natsu would jump in front of her and unleash a flurry of fire attacks like his 'Fire Dragon's Roar' to drive the enemies away.