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.
There might be some fanfictions that depict Natsu and Lucy sleeping together in a non - inappropriate way, like they could be sharing a room during a quest out of necessity and just sleeping in separate beds or something similar. But it can be hard to find ones that are completely pure in the vast world of fanfiction.
Their friends in the guild would likely be very supportive. Happy would probably be over the moon, flying around them and chirping happily. Erza might give them a stern but warm look and offer some words of advice about maintaining a healthy relationship. Gray would probably make some snarky comment at first but deep down be happy for them. And Wendy would be all smiles, seeing two of her favorite people find love with each other.
One interesting adventure could be when they end up in a parallel dimension. In this new world, they have to figure out how to get back home. Along the way, they meet strange creatures and learn new magic spells that are unique to that dimension.
One possible plot twist could be that they face a powerful enemy who has the ability to make them forget their feelings for each other. As they struggle to regain their memories and connection, they discover new things about themselves and their relationship. Another twist could be that there is a misunderstanding caused by a jealous third party, which leads them to briefly separate before realizing the truth and coming back together stronger. And a third plot twist might be that they are forced to choose between their relationship and a great power or responsibility that could change the fate of their world.
It could be about them having to take shelter during a storm and sleeping in the same small space, like a cave. But they respect each other's boundaries and just have a friendly conversation before falling asleep.