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.
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.
Goku is a pure - hearted and somewhat naive Saiyan when it comes to relationships. Launch, on the other hand, has her dual personalities. In a fanfiction, their different personalities can clash. For example, Goku's straightforwardness might annoy Launch's sweet side, while her tough side might find his naivete endearing. It could lead to some comical situations.
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 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.
Goku and Launch could start with a simple encounter involving lemons, like Goku accidentally bumping into Launch while she is carrying a basket of lemons. This could lead to an apology and then an invitation to share some lemonade. From there, their relationship could grow as they find more common interests related to lemons, such as making lemon pies together.
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.