Their relationship could develop through shared experiences. For instance, if they were to take part in a training session together, they would learn more about each other's strengths and weaknesses, and grow closer as a result.
One plot idea could be Jinora and Ikki going on a spiritual journey together. They might discover a hidden part of their world filled with ancient spirits. Another could be them facing a common enemy that threatens their family or the Air Nomad culture. For example, a dark force that aims to disrupt the balance of the elements.
The 'lemon' aspect might be a bit hard to come by in a clean way as it often involves inappropriate content. But for normal Korra and Mako fanfictions, you could also try FanFiction.net. Some stories there might show their relationship developing, their adventures together, and how they support each other, which can be really interesting to read.
Korra could meet the founders of the different bending disciplines. She could meet the first water benders and learn about the purest form of water bending. This would not only enhance her own skills but also give her a deeper connection to her water - bending heritage.
Archive of Our Own is a great place to start. It has a large collection of fanfictions, and you can easily filter out any inappropriate content. Just search for Korra and Mako, and you'll get a variety of stories exploring their relationship, from friendship to romance, all within the boundaries of a proper and respectful narrative.