I'm cool with them just hanging out doing normal stuff.

If you ever want something a bit deeper, there's the whole identify crisis stuff. Touma has amnesia and unlike many other stories, this never gets fixed. Both Touma and the narrative itself considers post and pre memory Touma to be two separate people. The narrative even calls his amnesia a death. And while there are many similarities, post and pre memory do act differently in subtle ways. It's not as extreme as what's going on with Lion (I'm just going off what I read from their app), but it is a connecting theme that could be explored between them.

Edit: Now that I think about, both became what they wanted to be after losing their previous selves.