Michael,
As I understand it, there's no actual violation of MIRANDA rights when the suspect has been informed of her rights (the right to remain silent, the right to have an attorney present), but chooses to talk anyway, without the lawyer present.
It's a stupid move to waive MIRANDA rights, but stupidity on the part of the suspect doesn't necessarily make the involved police officers dirty or incompetent.
Lois is just being Lois, here: she's stubborn and independent (as in: I'm perfectly capable of getting out of this jam on my own, thank you very much!'), and she has a tendency to jump into things first, and worry about the consequences later (at which point, she usually starts yelling for Superman).
Yes, it's a bad move. But isn't that true about a lot of the things we've seen Lois do on the show?
Sooner or later, she'll come to her senses and do the rational thing. Right now, though, she's just trying to protect a secret, and going about that in 'Mad Dog Lane on steroids' mode.
