One possible plotline could be that the Lake Trio discovers a threat to the world that Arceus is either unaware of or is causing (unintentionally perhaps). So they have to battle Arceus to stop this threat. Another could be that a powerful villain manipulates the Lake Trio into believing that Arceus is a danger and they must fight it.
In a fanfic, a plotline could be centered around the origin of the Lake Trio's powers in relation to Arceus. Maybe they were created by Arceus for a specific purpose, but over time they have developed their own wills. They could start to question Arceus' authority and this leads to a battle. Another idea is that a strange new power emerges in the Pokemon world that affects both the Lake Trio and Arceus. They both react differently to it, and their different reactions cause a rift that results in a battle. Or it could be a simple story of the Lake Trio wanting to test their limits against the most powerful Pokemon, Arceus, and thus initiate a battle.
In a fanfic, it really depends on how the writer wants to portray it. If the writer wants to emphasize the unique abilities of the Lake Trio and perhaps give them some sort of combined power boost, they could potentially defeat Arceus. However, Arceus has the advantage of being a creator - like figure in the Pokemon world. It has the ability to create and shape the world, which gives it a very high level of power. So, generally speaking, Arceus is more likely to be the victor, but in the world of fanfiction, anything can happen.
It's hard to say for sure. Arceus is super powerful as the creator Pokemon. But the Creation Trio also has some really strong abilities. So it could go either way depending on how the fanfic is written.
In fanfics, the battle between the Pokemon Creation Trio (Dialga, Palkia, Giratina) and Arceus can be really intense. Usually, Arceus is seen as the god - like Pokemon, but the Creation Trio also has incredible powers. Dialga controls time, Palkia controls space and Giratina rules over the distortion world. Their clash might be about power struggle or some sort of cosmic balance. It really depends on how the fanfic author wants to portray it.
A plotline could involve a special Pokemon that both Ash and Paul are interested in. They might compete to catch it, which could involve a series of challenges and battles. Or, perhaps there's a new type of Pokemon training technique that one discovers and the other tries to learn from or outdo. This could create an interesting dynamic in the fanfic.
A fanfic centered around the Pokemon Lake Trio in the Hall of Origins might involve a young trainer's journey. The trainer, curious about the legends of the Lake Trio, embarks on a quest to find the Hall of Origins. Once there, they discover that Uxie's knowledge is not easily accessible, Mesprit's emotions are overwhelming, and Azelf's protection is hard to bypass. But through determination and respect for the Pokemon, the trainer gradually uncovers the secrets of the Hall and forms a special bond with the Lake Trio.
A storyline might involve a group of trainers who are all affected by a strange phenomenon in the Pokemon world. They come together and decide to make a collective wish to Arceus for a solution. Arceus could then give them a quest that requires them to cooperate and use their unique skills and the powers of their Pokemon. As they progress through the quest, they discover the root cause of the phenomenon and are able to resolve it, thanks to Arceus' guidance.
One possible plotline could be a story of conflict and reconciliation. Giratina, often seen as the 'evil' or 'banished' Pokémon, might have some sort of misunderstanding or old grudge against Arceus, the creator. The fanfic could explore how they gradually come to understand each other's perspectives. Maybe there's a threat to the Pokémon world that only they can face together, forcing them to put aside their differences.
One idea could be a story where the Lake Trio's powers are being misused by an evil organization. A young trainer discovers this and teams up with the Lake Trio to stop them. For example, the organization might be trying to use Uxie's knowledge - granting power to create a super - weapon.
Well, in a fanfic, the Lake Trio could face a threat within the Hall of Origins. For example, an evil force might try to steal their powers. Uxie's knowledge could be used for wrongdoings if captured. Mesprit's emotions could be manipulated to cause chaos, and Azelf's protection could be weakened. The story could revolve around how the Lake Trio overcomes this threat with the help of a brave trainer or other Pokemon.
One possible plotline is that Ash is on a journey to prove himself against the toughest opponents and finally faces Brandon. He uses his Pikachu in a unique way to gain an edge in the battle.