What I was thinking after I signed off last night was this...
There was some confusion over what was said about the search for Lucas at the home when it said the sniffer dogs couldn't find a trail and they couldn't find him in the home. I think it was bad reporting grammar and they meant that the dogs couldn't find a trail and the officers doing an eyeball search, checking under beds, cupboards, etc couldn't find Lucas in the home or garden.
Then, I think the day before yesterday someone said that LE had gone back to the current address to do checks there? I kind of suspect that the return to that address was the full forensic and cadaver dog search. As far as I know sniffer dogs don't go into the home to check for a person's scent, something is brought out of the home for the dog to sniff and the dog starts at the last known location for the person, not inside the home but outside the front door or wherever they were last seen.
At the point of the return to the address, that roughly coincides with the arrest of EG, though I don't know if it was before or after (maybe they needed the arrest to get the warrant for the full forensics/cadaver dog check?) the LE activity seems to have changed focus. I fear they might actually have found something concerning in the home, in the car, at the old address (if they were going back and forth during the move)? It could be the weather that has caused no reports of LE outside activity recently, but it could also have changed for this reason if they're trying to switch to an intelligence-led investigation based on tips, talking to people, and what they found during those higher-level forensic searches.
The parks searching didn't seem like it was ping based or anything like a trail or sighting because they went from one park to another, and then to a third in a totally different area of town. Maybe someone overhearing that she went to the park could have caused those searches, or the FBI team might have suggested to start in those places, but I see it more like in the Mariah searches where LE were focused on bridges over creeks and small ponds for nearly a week before they hit on the right creek.
If it's something like EG claims to LE that on Saturday morning she took the kids to the park, maybe they'd check the parks, but then why would Lucas' shoes be at home? If he only has the green shoes that fit him at the moment, then something must have happened in the home (if EG is responsible) because he was only in socks and not in shoes.
I've also been trying to consider that if something happened in the home there might have been a re-dressing (a pm re-dressing).. Or that Lucas might not have been wearing those clothes when he went missing and they're a part of the alibi and have simply been thrown into a dumpster? But if the latter was the case, why the socks and not the shoes? This is partly why I want to know if it was common for Lucas to wear socks inside the home? There's one picture of him in the house that I saw with his feet showing and he had bare feet, so when does Lucas wear socks but not shoes? Did something happen while he was getting ready for bed and he wears socks to bed? Did something happen when they were getting ready to go out and he had his socks on but not his shoes? If EG wanted things to appear that Lucas had wandered off, why didn't she put the shoes on or throw them in a dumpster, why leave them in the home yet say Lucas was wearing socks?
I don't have any potential answers to these questions, but they stand out to me, and I wonder if anyone else here might be able to work with them and come up with some ideas?