One common theme is the discovery of love. Goku, being somewhat naive in matters of the heart, gradually realizes his feelings for Launch. Another theme is adventure. They often go on quests together, which strengthens their bond.
There are quite a few. In some fanfictions, they meet in unusual circumstances. Maybe Goku saves Launch from a bad situation, and that sparks the start of their relationship. It's a unique take on the characters as they both have such distinct traits.
One possible plot could be that Goku and Launch meet in an unexpected place, like a new planet during one of Goku's adventures. They start as strangers but gradually form a bond as they face common enemies together. Launch's dual personality could add an interesting twist, with her sweet side being attracted to Goku's pure heart, and her more aggressive side coming out to protect him when in danger.
You can focus on their adventures. For example, they could team up to find a magical item that has been lost. Along the way, they encounter various friendly creatures and face some challenges that require both Goku's strength and Launch's cleverness to overcome. There's no need for any inappropriate content, just good - hearted, exciting adventures.
Another possible main character could be the villain that forces the two Gokus to meet. This villain could be a new, super - powerful threat that the two Gokus need to deal with. Their meeting becomes a crucial part of the story to defeat this powerful foe.
One popular 'goku x launch fanfic' is 'The Unlikely Bond'. It explores their relationship in a unique way, with Goku slowly realizing his feelings for Launch. Another is 'A New Beginning' which focuses on how they team up against a new threat and in the process, their relationship deepens.
One idea could be that Goku discovers Launch's secret love for lemon-flavored treats during a training break. They bond over sharing some lemon candies and it leads to a friendly competition to see who can endure the most sour lemonade. This simple shared interest could strengthen their friendship in the fanfiction.
You can try some popular fanfiction websites like FanFiction.net or Archive of Our Own. They usually have a wide range of Dragon Ball related fanfictions, including ones about Goku and Launch's relationship.
A really interesting plot could be set in an alternate universe where Goku and Launch are arranged to be married for some political reason in the Saiyan or Earthling world. They start off not really liking each other but as they face challenges together, they fall in love. For example, they have to deal with a group that is against their union and in the process, they learn about each other's strengths and weaknesses.