Honorifics are crazy important in some Asian languages. Not sounding polite/respectful enough when talking to someone can be seen as a small or huge insult depending on how you speak.
While dono does mean something akin to 'lord' or 'lady' - it is not any indicator nobility or royalty. It just means that the speaker and the person they are speaking to have the same high rank socially, but the speaker is still trying to be super polite to the person they're addressing. Since Yugiri is leader of the Doman refugees and Alphinaud is one of the quasi-leaders of Scions and eventually becomes the leader of the Crystal Braves -- it makes sense why he would use 'dono' while addressing her. He respects her, but he views himself as on the same level as her.
If she were of higher standing socially, Alphie would have had to use 'sama' - otherwise he would have been seen as being a prat for not humbling himself enough in Japanese conversation.
While dono does mean something akin to 'lord' or 'lady' - it is not any indicator nobility or royalty. It just means that the speaker and the person they are speaking to have the same high rank socially, but the speaker is still trying to be super polite to the person they're addressing. Since Yugiri is leader of the Doman refugees and Alphinaud is one of the quasi-leaders of Scions and eventually becomes the leader of the Crystal Braves -- it makes sense why he would use 'dono' while addressing her. He respects her, but he views himself as on the same level as her.
If she were of higher standing socially, Alphie would have had to use 'sama' - otherwise he would have been seen as being a prat for not humbling himself enough in Japanese conversation.