denuseri, you appear to be arguing for a downgrading of the breach in trust badkitty showed. I'm sure that's not what you meant in your reply.
I agree, Dragon, the lie is significant, much more so than the original infraction. Are you r/l or o/l? It makes a difference in terms of punishment I'd suggest.
If r/l, I'd suggest a complete loss of priviledge at home. Except for when she has to go out (work, for example), or when she's doing chores, I'd have her spend her time sitting in a corner, contemplating what she has done, and what it means. The end result of her 'penance' should be a long, well though out, well written explanation of precisely what a breach in trust means, and why it is so very wrong. I would accept no less than 5000 words, and would expect something very thoughtful and incisive. While that was being written, I would ban her from speaking to me unless I asked her a question, or commanded her to speak (if she needs the toilet, she'd wait until I asked her if she needed to go, for example).
The penance would last as long as it takes to provide a suitable document, and in no instance would it last less than a week.
You could try that o/l, but managing it would be hard.