A "luxury" can mean something like a fine watch or car: something expensive, something everyone would like to have, something nobody actually needs. "We don't have that luxury" is an idiomatic phrase that's often used by an authority when turning down a request. Instead of saying "no," the authority can say "I'd like to, but I can't," and one way to say it is "we don't have that luxury. Calling something a "luxury" is saying that it is not needed, that it is a crazy dream, it's unrealistic. It is contrasting the "luxury" with harsh reality. "Don't be silly." "We don't have that luxury." Here, the idea is that responding only to what has actually happened, and hoping that it is the last, would be nice--a "luxury"--but impossibly unrealistic.

I think it's something closer to "can't afford to": "Law enforcement can't afford to make the assumption that there won’t be additional attacks." It would be nice if they could, meaning there would be no further danger, but that idea is just a luxury.

In this case, the phrase "doesn't have the luxury" means simply "doesn't have the right", so all this statement would mean that "Law enforcement should not make the assumption that there won't be additional attacks."