VERY long post ahead!
I agree with you that she is seriously messed up in the head. As a longtime field diagnostician, perhaps I can help with one aspect of your post.
Being diagnosed within the context of DSM-5 is for treatment and clinical study only. It has absolutely nothing to do with the legal definition of insanity. There's a really great series of shows on S5 of St Elsewhere about this very issue.
A person can be schizophrenic and still stand trial. A person can be a flaming malignant NPD and still stand trial. And a person can be a pedophile (per DSM) and obviously, still stand trial. Drug abuse is in DSM (and is a mental/neurological disorder). Alcoholism is in DSM (and a mental/neurological disorder).
You might be surprised to know what kinds of questions psychiatrists actually ask to determine whether a person is "mentally competent to stand trial," which is an entirely different issue than "do they have a treatable psychiatric or neurologic illness?"
They start with such things as, "Do you know what day of the week it is? What month of the year? What year is it?" Usually, people get those right. A complete non-response to those questions will result in a different kind of further evaluation (does this person ever answer questions? do they know their name?) Even really uncooperative people will sullenly acknowledge their name. If not, then they are under close observation when they interact with other patients or their attorney or their parents. Oddly, all of a sudden, nearly everyone seems to remember their name (and their provisional diagnosis, "malingering" is not enough to keep them out of court or give them an insanity defense - kind of the opposite).
Is it good and moral to murder people without provocation? Yes or no. There are a lot of yes or no questions. If the person ever wants to see the outside of an institution, they will have passed the above part of the exam (they know what month and year it is, anyway, they know their name).
Is it a good thing to murder a child? Yes or no.
Is it good or permissible to murder a child who is placed in your care and to whom you acted as mother? Yes or no.
The doctor will keep going back to "yes or no" and repeating these hypothetical questions. They may throw in some interesting ones. "Is it okay and good to keep an unregistered gun in your handbag at a school?" "Is it good and lawful to buy a gun that has had its serial numbers removed?" For the more intelligent antisocials, they can't resist showing that they do know the law.
And when they do that - they get to go to trial and they do not get an insanity defense. Judges review all of this material very carefully and criminal defense attorneys know all of this better than I do.
"Is it good and permissible to legally buy a gun, with the sole purpose of intending to kill your husband?" (Actual question asked in a case I'm familiar with). "Yes," said the wife. "Is it good and permissible to premeditate the murder of your abusive husband?" "Yes," said the wife. At that point, it now became a matter of a jury trial. This person claimed her husband was abusive, but he was not in the same room or even in the house when she shot him and then hid the weapon. She then lied to police about an intruder in the yard.
Defense tried the battered spouse defense, and they lost (jury didn't buy it).
But notice how this person was able to answer simple questions that showed her mind was working and that she had a sense of right and wrong (even if the rest of us don't agree).
Personally, I think LS's own approach to these exams will be to adopt that meek demeanor we saw at her extradition proceeding, pretend not to understand everything, but ultimately answer, "Yes, I know it's wrong to stick children in freezers" or whatever else they may ask. Usually, they use questions that are not directly applicable to the situation at hand, just to test a person's sense of right and wrong.
"I don't know" is a valid answer, and gets the person more time in the psych ward. A person with a DSM diagnosis AND a track record of stating plainly that the "don't know that it's wrong to bomb schools" (or whatever gets asked) is definitely a risk to themselves and others.
"Would it be wrong to...X" is often the form asked if it's clear the person understands ordinary English. In this case, LS's educational background (alleged) will cause the psychiatrist to asked tougher questions, as she should be able to answer them. Since she is a blabbermouth, I predict she will answer, but have a hard time sticking to yes or no, but will eventually commit to a short answer.
None of this ever comes before the jury, nor would Al or Landen get to know what she said. BTW, learning to do a mental status exam is something that many different professionals are taught to do (including techs in ER's with a 2 year college degree). Doing a complex mental status exam in a felony murder case will be done by an experienced psychiatrist or two or three.
One of the best psychiatrists I observed would throw in these seemingly random questions near the beginning, "You're driving in your car, you see a dog in the road, is it okay or right to deliberately swerve to hit the dog?" They always answered "no." Everyone knows that! He knew right then and there the person knew right from wrong, and this one involved a bit of critical thinking - so they're clearly able to understand human speech and use their mental faculties to answer.
They're not legally insane.
and the officer that she attacked on the return trip to CO also knows what she's capable of. 
