I didn't want to speak too soon, but it seems safe now to say that we have our normal child back. The popular theory (among Doug and myself, at least) is that the insanity was the indirect result of the oral albuterol that Lila was taking for a few days. The pharmacist warned me that it could make her hyper and she might have trouble sleeping.
We started giving it to her last Thursday night and she seemed to sleep fine. And then, on Friday afternoon, she turned into the devil. So we think that what happened was that the albuterol was keeping her from sleeping well and she, therefore, became severely over-tired. The rest is history. She was mostly back to normal on Tuesday and by today she is the same old Lila we used to know.
That's not to say that she has entirely given up on throwing fits, but she was already doing a bit of that before The Incident. Right now, she is gleefully playing with her Daddy's belly button and chest hair. I'm waiting for the day that she decides to pull the chest hair. Mwahahahaha!