It ended up as a confrontation.
Lyn expected it; the only way anybody could stop him is to fight him. So when Kazuya made the first move and attacked her, Lyn already had her blade ready.
Though she feigned and acted indifferent about it for so many years, Lyn always wondered how it would feel to be normal, to lead a normal life. If she was just the average Princess who they raised with a silver spoon in her mouth would she have ended up exactly like her siblings? Who dedicates themselves to the country? Then again, it's not like she isn't committed to the country. She loves this place and the people living here though she has made little contact with the outside.
The little times Lyn goes out, she treasures every moment and interaction. She wants to help these people, but as 'Lyn' and not a Princess. With this goal in mind, Lyn stopped caring about her isolation. At least on the surface, once in a while, she experimented with the idea.