Themes like roommate drama are quite common. There could be conflicts over things like sharing the apartment space or who gets to use the TV at a certain time. Also, there are fanfictions that focus on how they support each other in their careers. For instance, Leonard helping Sheldon with a big research project or vice versa.
Well, Tumblr also has some really interesting Sheldon x Leonard fanfiction. Some of these fanfictions delve deep into their emotional bond. For example, there could be stories where Leonard helps Sheldon through a difficult time, and in the process, their relationship evolves in unexpected and heartwarming ways.
Leonard would probably be shocked at first. If he's in a good place in his own relationship, he might be more accepting. But if not, it could stir up old feelings of jealousy. However, in the long run, depending on how Sheldon and Penny handle it, Leonard could come to accept it and they could all find a new normal in their friendship group. For example, if Sheldon and Penny are happy together, Leonard might see that and be happy for them despite the initial shock.
Often, they communicate more openly. For instance, Leonard might finally tell Sheldon that his constant nitpicking is getting on his nerves. Sheldon, in turn, realizes he needs to be more aware of Leonard's feelings. They start to make compromises. Like when they want to choose a TV show to watch, they take turns instead of Sheldon always getting his way.
One great story could be about Sheldon and Leonard having a 'bro day'. They might go to a science convention together, and along the way, Sheldon starts to understand Leonard's need for a bit more social interaction. He tries his best to be more 'normal' in public, like not correcting every little scientific inaccuracy he hears. This shows their growth in their relationship.
The uniqueness of their relationship. Tam and Sheldon are both very different characters. Sheldon is extremely intelligent but socially awkward, while Tam has his own set of qualities. Fanfictions that explore how they interact and complement each other are special. For example, Tam could help Sheldon in social situations that he struggles with, like understanding group dynamics at school.
Perhaps an intelligent and patient psychologist. She could help Sheldon understand his emotions better. Given Sheldon's complex personality, she would need to be very understanding and be able to handle his idiosyncrasies. This type of girlfriend could also introduce Sheldon to the world of human emotions in a more systematic way.