It's not possible to go around the lake in a loop. Sending a child alone to search the SE tip of the lake meant driving around to the Maiden Lane area to pick him up. With one child already missing, who in their right mind would do that?
The other girl that was late with Lyric was her 11 year old cousin. They were late and apparently when a parent looked for them at the park where they were allowed to be, the parent could not find them ... so police were called, but just at that moment, Lyric and Tammy's 11 year old daughter walked through the front door. Tammy was probably thinking of "cool" places (like a favorite aunt) that her daughter and Lyric would visit, like the park, the lake ... and it turmed out Lyric and Elizabeth did possibly ride their bikes to the lake. The fact that Lyric went to a park with her older cousin a week earlier and she didn't follow the rules implies that she may have done the same thing with Elizabeth ... perhaps they rode their bikes to the lake.
Perhaps they were last seen at12:11 and the camera was 8 minutes slow in relation to the cyclist's cell phone. So, 12:19 on video heading west behind the Cornbelt Auction. If the cyclist's sighting is accurate, then (children their age cycle at an ave. speed of 9 MPH) it was 8 minutes later at 12:27 that he swerved around their bikes ... so they had already arrived and vanished.
"How long were the family members at the lake before someone went to the police station?"
An hour? I admit to being guilty of letting three hours pass when my 13 year old son was supposed to be with a friend in a safe place. All turned out well.
Skateboard park seems too public for an abduction.