I read an interesting article about the Miranda case and Miranda rights once (wish I could remember everything), but the gist of it was:

1) The Supreme Court took on the case (was it Miranda vs. Arizona?) because there was much confusion about what legally could be done to elicit confessions from crime suspects, and whether or not these confessions were legally admissible as evidence.

2) As a previous poster mentioned, "you have the right to remain silent" and the arresting officers must tell you that. But if you choose not to remain silent, (as the next part of the speech goes) "anything you say can/may be used against you in a court of law." (forgot the exact wording.) So in general, if you're faced with being arrested for a felony, SHUT UP. Let your lawyer do the talking.

Good job with the fic, explaining that Lois doesn't want her lawyer there because of the Superman secret. Very plausible. Although not so good for Lois. But, as previous posters have also mentioned, that's very in-character for Lois.