A few things...just my thoughts.
Given how fast this seems to have happened from pick-up at the park to the fire in the backyard, with her phone being turned off within minutes of the pick-up, it's entirely plausible to me that she was likely incapacitated somehow straight away. There are people who are strictly interested in the end game, and they can go from "Hey, nice to see ya", to a hard hit or other blunt force injury to disable someone and immediately remove resistance from the equation. As Otto mentioned, both Jesse Matthews and Bundy are examples of that type of brute behavior. And often, part of the preference of these kinds of people is to render the victim utterly powerless from the beginning. Nothing strips a person of all power like being made unconscious. Even temporarily for the perp to engage in additional and easier methods of restraining or controlling. Some have said that wouldn't happen because the Lyft person might have seen it or wasn't fully out of sight. I would imagine that any Lyft driver is focused on safely delivering the passenger at the right address, then moving on to whatever comes next in their tasks. So, once the driver was driving and headed off, AA was in the clear. If the Lyft driver didn't notice, or couldn't tell the description of the person picking her up, or the car he was in, he wouldn't discern much about to happen or happening in the car as he drove off (not his fault or failure). I think AA got control of her and her phone pretty immediately.
Plus, we don't know that she had agreed to go to his home, nor do we know if he was even telling her the truth about his lifestyle, type of residence, etc. She would have been very aware on the drive to his house that he was not headed toward a place or section of town that was consistent with any other plan they discussed. So, he would have to subdue her early on to not have a hassle. If they had done this before, that goes out the window, because she might have already been to his house. My guess is LE knows the nature of communication between them and already has that part answered.
As far as his "girlfriend" remarks and secret room mission, etc., I'm a firm believer that people's words betray them, and especially narcissistic types. Who would care why he wanted a construction job done and whether or not she's white and Morman? Why is that relevant when you're hiring a contractor? That may simply have been him 'storying' himself and fantasizing about what was rolling around in his sick head about what he hoped or planned to do in what has turned out to be this crime. Also, have had the tragic experience of knowing a narcissist/sociopath/dark triad, or whatever we call these types of individuals, and the bold lying they do because of the false reality they invent in their minds is stunning to the average person, because it's just so high risk and nuts. I have nothing on my phone log to hide, but if I had done something this utterly heinous, I sure as heck would not try to fly a claim that I talked to the person the day before, but not after, when it's so easily determined to be a lie. How can anyone in this day and time not know that there is a footprint of anything you do on a cell phone or other device?
My ugly and sad experience with this kind of personality is that they are both boldly dishonest because they think they have all the control, and simply reject or override facts and evidence placed before them as to their lying. They go to the place in their head where their story of themselves is, and they tell you, or police, or whoever, that their story is simply how it is. Alongside this is that these kinds of people have a dullness to them and a sort of density they can't ever fully overcome. This explains why he could be so unaffected when asked about the fire, saying that he was "almost done", as he burned a body and evidence right in front of God and everybody. They just don't see that they are not invincible, or that their incomplete ideas and story about their actions is doomed to fail. Some of the smarter ones might get away with it for a time, but when they're caught, you can see into what dum-dums they truly are. They're just missing some wiring and software, they just are. I've witnessed this personally, and I still stand amazed. FWIW