A common theme is redemption. Many fanfictions explore the idea of Gaea being redeemed through her interaction with Percy. Since Percy is often seen as a symbol of hope and goodness in the original series, his influence on Gaea can be a way to show that even the most malevolent beings can change.
In this fanfiction, perhaps Gaea discovers a way to use the chakra in Naruto's world to strengthen her own power. She sends her minions to capture ninja who are strong in chakra. Percy Jackson, who has a connection to the spirit world, senses this disturbance and travels to Naruto's world. Naruto and Percy meet and realize they have to work together. They gather allies from both worlds, like Naruto's friends from Konoha and Percy's demigod friends, and fight against Gaea and her forces.
Well, it's not as popular as some other pairings in the Percy Jackson fandom. Gaea is a major antagonist in the series, and the idea of her in a romantic relationship with Percy is rather unorthodox. So, compared to more common pairings like Percy and Annabeth, it has a much smaller following.
One good Percy x Gaea fanfiction could be 'The Unlikely Alliance'. It explores a scenario where Percy and Gaea are forced to work together due to some strange magic that binds their fates. It has interesting character development as Percy tries to understand Gaea's motives beyond her typical 'destroy the world' stance.
One great 'Percy Jackson Gaea' fanfiction is 'The Battle Against Gaea's Wrath'. It continues the story after the end of the main series, with Percy and his friends facing new threats related to Gaea. The author does an amazing job of keeping the characters' personalities intact.
One possible fanfiction could be about Percy Jackson having a strange encounter with Gaea's power while in a lemon grove. Maybe the lemon trees are enchanted by Gaea, and Percy has to figure out how to break the spell without getting caught in Gaea's grander plans for chaos.
In the Percy Jackson series, Gaea is a villain, and a love relationship between Percy and her in the context of the original story is very unlikely. However, in the world of fanfiction, anything can be created. There might be some fanfictions exploring such a strange and dark concept, but it would be a very unorthodox take on the characters.
In a fanfic, Percy could have a mental battle with Gaea where the lemon plays a key role. Imagine Percy enters Gaea's mind - realm. There, he finds a withered lemon tree. By using his willpower and connection to the ocean (as water is also related to life like the lemon), he tries to revive the tree. As he does this, Gaea is forced to watch and is affected by his actions. If he succeeds in making the tree bloom again, it could signify his victory over Gaea's destructive plans.
Well, it could be a really wild ride. Percy joining Gaea would be such a shock to his friends. They would probably think he's been brainwashed. And Percy himself might be in for a rude awakening when he sees Gaea's true intentions. She could be using him to get to other demigods, or to start a war between the gods and the demigods. He'd have to figure out a way to break free from her influence before it's too late.
One common theme is identity struggle. Since Percy is known as the son of Poseidon in the original, being the son of Gaea in fanfiction makes him question who he really is. Another theme is power and its consequences. With a different origin, he has different powers and has to deal with how they affect him and those around him.