I always thought the song "Don't Speak" by NoDoubt is an appropriate song for Rune and Alys. From the introduction of Rune, Alys seems slightly bitter towards him, and a romantic past between the two of them is insinuated.
So, since Rune and Alys were separated for a time (in my imagination, I think it is due to his duty as Lutz) Rune had to leave Alys for a time. My interpretation is that the scene was a heartbreaking one, and that is where the song comes in.
I can imagine a hard-edge guy like Zio listening to heavy metal, so I imagine "I Don't Care" by Apocalyptica being his song, as he has no care when killing an innocent woman like Alys.