People who are mentally incompetent, are still capable of lying.
Demonstrating that they are competent enough to understand that they believe they will avoid moral/legal dilemmas by lying rather than by telling the truth in that particular circumstance.
This isn’t a legitimately mentally ill person; this is someone who is trying to avoid the consequences of her actions. A truly mentally ill person who *truly* did not understand that she should not mail a live dog in that matter would have said “a poodle”, “a puppy” or “a dog”. She would have told the truth because she would not conceive of any reason to lie about the contents.
This person understood that she could not mail live animals in that manner. That is why she lied.