No. I absolutely do not think this is Lance-Adams syndrome.
I think she suffered a very prolonged episode of anoxia due to drowning, followed by cardiorespiratory arrest, followed by a long course of CPR/ ACLS resuscitation. I think her brain is irreversibly, terminally damaged. I think the "best" that can be hoped for is PVS on a ventilator. Because she was able to have her heart resuscitated, and had access to a top notch neuro ICU, she received every possible level of care and treatment-- far more than most non-celebrities would likely receive in similar circumstances. But it's my opinion that she will die relatively soon. I think that support will have to be withdrawn. I'm not a talking head, so I can say that. I'm sorry that's very blunt. I don't mean to sound "cold", but this is really a hopeless situation, soaked in drama from the money, and celebrities, and rumors about criminal charges.
I know many people like to hold out hope for a miraculous recovery, but I don't think that's even remotely possible here. IMO, any hope of her waking up, and breathing, and being able to be aware, and interacting with loved ones (let alone returning to her old self) is in the category of "unrealistic hope." The statistics don't lie, and her situation is overwhelmingly hopeless. It's just taking a month or so to demonstrate that.
She died in that bathtub. She was discovered soon enough that her heart was resuscitated, and she had "some" brain function, albeit heavily damaged by anoxic cerebral encephalopathy. She has been dying an agonizingly slow "second death" secondary to her resuscitation, for the last 3 1/2 weeks. IMO.
Remember that large retrospective study I posted about, of 1669 adult near drowning victims with cardiac arrest at the scene? 1641 of them died at the scene, or in transit, or in the ER. 28 were resuscitated to a heartbeat and admitted to ICU. Roughly 26-27 of those 28 died during the course of hospitalization (less than a month, IIRC). 1 or 2 (equivalent statistically) survived to PVS. I don't think BK will make it to chronic PVS, if her status epilepticus is this profound at 3 1/2 weeks and 2 attempts to resolve the cerebral depressant coma.
Her prognosis is very, very grim. I believe she will die, and that is a tremendous tragedy for a beautiful 21 year old young woman, in the prime of her life. I don't know how many other statistics I can pull and post to demonstrate that, if the ones I've posted so far aren't persuasive.