I admit that I haven’t read everything on this thread, but I am confused about why you say that someone asked Lyric and Elizabeth to meet at the lake, park their bikes and throw her purse over the fence. Is there any evidence that the girls were told to do these things and DID them vs a perpetrator doing these things?
At the time of the disappearance, a couple of other WS members and I studied every aspect of how the girls ended up at the lake. The computer that I used at the time is long gone, as are the maps. However, going from memory ...
The girls told their grandmother that they were going to cycle in the nearby alley (CCTV behind auction house) and at the nearby shopping mall. Elizabeth had a friend who lived near Meyer's Lake, and the girls were seen cycling at the corner of that street by a man mowing his lawn. Elizabeth knew the route.
They continued cycling towards the bike trail that goes around the lake. That is where it's uncertain whether they went into the trees near the lake, and a third party walked their bikes over to the gate (not likely), or they cycled on the path and parked their bikes at the path-side of the gate before crossing to the water-side of the gate. There are no witnesses after the lawn mowing man.
My conclusion was that, after cycling in the alley, they seemed to rather intentionally, and in a short amount of time, cycle to the Meyer's Lake gate on the far side of the lake, park their bikes, cross to the water side of the gate, and vanish. Lizzie's purse, with a semi-functioning cell phone, was left behind near the shore.
The pathway was used by other cyclists and joggers that day at that time. No one saw the girls, or anyone else with the bikes. Someone placing the bikes at that location risked being seen. It would be safer to leave the bikes in the small nearby forest - which is where a vehicle may have been parked, hidden from the street. There's a service road into the treed area.
At the time, I think many of us wondered what lured them to that specific location simply because they seemed to race directly there, park their bikes and that was it. It's hard to say - but the question is: what cause them to disobey or mislead their grandmother and race to the lake? Why park their bikes if they knew their grandmother was expecting them back right away? Why go to that rather deserted part of the lake if they were just going to follow Lizzie's route to her friend's house?
Given the tight timeline, the bikes were placed there at the time of abduction, not after the girls were murdered.
Google Maps