A plot could start with Latias being in some kind of danger, and Ash comes to her rescue. This leads to them spending more time together. As they get to know each other better, they realize their feelings are more than just friendship. After getting married, they might have to deal with people or Pokemon who don't approve of their relationship at first. But through their kindness and the strength of their love, they win them over and continue their happy life together.
Ash could catch Latias in a place full of ancient ruins. Latias might be guarding some sort of Pokemon relic there. Ash shows respect for the place and Latias' role. This makes Latias interested in him. Eventually, Ash catches Latias and they go on to discover more about the relic's power together.
Yes, there are some out there. You can start by looking on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'pokemon ash and latias married' in their search bars, and you should be able to find some stories. However, the quality may vary, so be prepared to skim through a few to find one that suits your taste.
The plot could involve a threat to Alola. Ash and Lillie, now in love and getting married, have to put their wedding plans on hold to save the region. Along the way, they discover that their love gives them extra strength. They defeat the threat together and then have a grand wedding celebration, which is attended by Pokemon trainers from all over the world.
One possible plot could be that Ash and Ursula meet during one of Ash's travels. They start off as rivals but gradually develop feelings for each other. After many adventures together, they decide to get married. Their wedding could be attended by all their Pokémon friends, and they might start a new life exploring new regions as a married couple.
In this fanfiction, it could be that Ash's marriage is a way to bring peace between different regions. He marries a princess or a powerful trainer from a rival region. Their union symbolizes the unity of Pokémon trainers everywhere. The story could then detail the political and social implications of their marriage, as well as the more personal aspects like their relationship building and how they learn to love and respect each other's Pokémon.
In this fanfiction, it might be that Latias controls Ash as part of an experiment. Latias is a curious Pokémon and wants to see how a human like Ash would react in different scenarios. So she uses her powers to make Ash explore areas he might not have otherwise, like a hidden and mysterious part of the Pokémon world. This could lead to Ash discovering new Pokémon species or even new types of Poké Balls. As he's being controlled, his initial fear turns into a sense of adventure as he experiences things he never thought possible.
One possible plot could be that Latias discovers she is pregnant and has to hide from some villains who might want to harm her unborn child. She could then seek help from other friendly Pokemon or trainers.
One plot idea could be them training a new and rare Pokemon together as a married couple. Another could be them hosting a Pokemon tournament in their hometown.
One possible plot could be that there is some sort of a prophecy in the Pokémon world that foretells the birth of a special baby from a human and a legendary Pokémon like Latias. Ash gets involved in this prophecy without knowing at first. As the relationship between Ash and Latias develops, they find out about the baby. The baby could have a great destiny, like being the bridge between different Pokémon species and humans. Ash would have to teach the baby about the values he believes in, like friendship and perseverance.
Well, it could be that Latias has been influenced by an ancient prophecy. According to this prophecy, Ash is the key to unlocking a great power. But she can't just ask Ash to come with her as she fears he will be stopped by his friends or other Pokémon trainers. So, she decides to kidnap him. As time passes, Ash manages to communicate with Latias and understand her motives. He then decides to cooperate with her, not because he has to, but because he realizes the importance of the situation.