@gregger : The way I understand it.
Prince told his dad he need to 'apologize' to the elf king for something, but say he won't say what (andwhy Lanciel is injured) until Lana and Souya are there.
Lanciel warn Souya of the underlying politic at work:
Since the incident involve a fight, with the overall 'winner' would be either the prince (yeah it was underhanded but that's not the point) or Souya who defeated him.
Regardless of who you point it to, Lana 'lost' to a human (Souya who defeated someone she couldn't, solo, or the prince who defeated her)
Elven pride damaged, if Lana's dad doesn't demand punishment the more prideful of the elves would likely revolt.
But if the father demand punishment it'll strain relation with the human nation, potentially starting the war from that side.
Either way, asshole prince get his revenge.
And the human king can't stay quiet on this one without getting to the depth of this not because of the prince but because Lanciel is injured.
Lanciel as it turns out is the daughter of the king's party member that died protecting him, whatever happened the king felt enough gratitude that he put the silver fox as the symbol of the mother on THE national flag and probably would've adopted Lanciel to be a princess if not for the law.
So Lana here is trying to solve the situation on both side by naming Souya as her husbando.
On the elven side, he would be someone technically in their 'family', maybe adding on that his skill was from her ancestor so in a way it was 'an elf' who defeated the prince.
On the human side, it was an honorable duel so eh.