If Lucy never joined Fairy Tail, the friendships and relationships among the characters would form in a very different way. Also, many of the story arcs might not unfold as they do in the original plot.
The guild as a whole would likely mobilize. Erza would start formulating a strategic plan. She'd consider the strengths and weaknesses of Acnologia and figure out the best way to approach the situation. Gray would also be ready to fight, using his ice - make magic to support the rescue mission. They would all be united in their determination to get Lucy back safely.
One popular theme is Lucy's growth as a wizard. Fans often explore how she overcomes new challenges and becomes stronger. Another theme is her relationships, not just romantic ones but also her friendships within the guild. For example, her bond with Natsu and how they support each other through tough times.
She would fit in very well. The Fairy Tail guild is all about family and acceptance. Given her parents are Lucy and Natsu, she'd be welcomed with open arms. She could learn from the older members like Makarov and Mirajane, and bond with the younger ones like Romeo. Her magic skills would also contribute to the guild's strength during battles or when helping the town.
Naruto would probably be very enthusiastic and friendly towards Lucy right away. He might be curious about her celestial spirit keys and ask a lot of questions. Lucy, on the other hand, might be a bit more cautious at first but would be drawn to Naruto's positive energy.
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.
Lucy could save everyone by making a great sacrifice. Maybe she gives up her magic power temporarily or even permanently to stop an evil force. In fanfiction, this could be something really emotional. She might be the only one who can access a certain magical item or place because of her Celestial Spirit keys. By using this advantage, she gets to the root of the problem and saves the day.
In some fanfiction, Bickslow teases Lucy a lot, which is his way of showing he likes her presence. He might make fun of her in a light - hearted way about how she gets flustered around Natsu.
In some fanfictions, Lucy might use her Celestial Spirit magic. For example, she could summon a powerful spirit like Leo to help fight off whatever is threatening Natsu. The spirit could provide a distraction or directly combat the enemy while Lucy tries to reach Natsu and get him to safety.
Her relationship with Natsu would likely change. Natsu might be initially distrustful of Lucy if he senses her connection to End, since End is often seen as an enemy. But then as he realizes that Lucy is still the same person deep down, their bond could become even stronger as he helps her control this new aspect of herself.