Keith says the charge was unjust. He was blamed for trying to sabotage the peace treaty between the Galra Empior and Altea Empior. He knows he didn't. He's probably the most pro-Altean Galra out there!
He managed to escape the police department he was being interned at between moving prisons, and now he's on the run. He decided, what better thing to do than flee to Altea itself? Plenty of Galra were living there since both empires were on good terms, as well as Alteans in the Galra Empior. He had his own space ship, and his own way to cover himself, do it seemed like the best plan out there.
Going under the name Kai (a name his mother always loved), he'd been living peacefully in hiding in whatever place he could find to stay that night on Altea. That is, until a cute Altean boy meets him at his job, and insists he come back to his "home". The "home" that just so happened to turn out to be the castle, and this cute boy turned out to be Prince Lance, the Altean hire.
Did he mention he may have fallen for this boy in the middle of all this?