Thank you for the ask @cinlat! Answering for the tag game: Lyna :D
In headcanon, Rigel becomes quite fond of Lyna, to the point where she asks Lyna to teach her the dancer weapon. I think they would have a lot to talk about with their respective worlds, and would have a lot of mutual respect of each other's battle prowess and courage. I think Rigel would also realize that just like her, Lyna has so much riding on her shoulders and has to watch some of her compatriots fall - and they would also be able to empathize with each other. So by the time Rigel left the First, these two would have been friends.
If Rigel did not have a loving partner waiting at home for her, or had been on the First from the beginning, this is a pairing I think I could have written for her. I think all the things that Rigel likes and respects about Lyna could have blossomed into attraction for her. But with Lucia in the picture, albeit in the Source, Rigel would have never started down that road. And I think she would have been very cognizant about the fact that she was going to eventually leave and go back to the Source herself, and thus would have been somewhat reluctant to start something serious knowing it would have to be cut off.
I love Lyna myself and really hope she will show up in some side content when Rigel visits the First down the road.