One: The general had ACTUALLY violated Lucas's rights.
Two: Lucas is Brazilian. The American military may have an "honorable" history of never actually attacking its own people. The Brazilian one does not.
Three: Lucas IS, yes, prejudiced against soldiers. And when a team of them violated the rights of Lucas to privacy, the rights of her country (Brazil) to sovereignty and threatened Lilly, surprise, surprise, those prejudices came out in full force. OF COURSE Lucas is pissed. There's nothing that pisses her off more than military overreach. Guess what she saw happening.
Lucas isn't perfect. She is, yes, prejudiced against militaries. And the general had just gone and done all he could to justify those prejudices. So, yes, of course Lucas is overreacting. Because, in that situation, that is what she would do.