Here's how I possibly envision the scenario:
Maybe Lucas was supposed to "eat his vegetables",or "drink his milk", or "clean his room" (idk) and was left there as punishment alone. Maybe EG says "when I get back you better have..."., and unleashes when she gets home when he hasn't done whatever she wanted him to do (thinking of Malik, Sherin...).
Or, she goes to Olive Garden because she is meeting a man in the process and wanted to keep it from Lucas/didn't want to be around him. (Again, to whom were those phone calls?)
Whatever the case, she gets home and becomes violent with Lucas as usual this time he dies.
Now, would she automatically go bury him or dispose of him right away? I think not, especially if it was not premeditated (judging from other cases, bodies are often kept overnight in the home, ex Hailey Owens and Jessica Ridgeway (different types of cases obviously though).
So, she keeps him there in the house with him overnight (garage? blanket? box...) while she thinks about what to do with him (likely getting very high/drunk). Maybe cleaning up during this time and trying to come up with her story.
She maybe decides that it would not be good to dispose of him during daylight for fear of being seen, so goes for a drive in the early morning hours before daylight (what time was sunrise?).
She then comes home and sleeps, or cleans up. Then calls 911.
This is one rough theory of how it could gave gone down imo, assuming there was no other man present.
(Hey, what if she's a lesbian/bisexual? Lol...maybe she's seeing a other woman haha)
Theory B would be, assuming she was alone, is that something happened in the morning.
As for the shoes, maybe that comment was made because LE clearly saw (and EG indicated as such) that Lucas' shoes were home...but still, why "running" specifically?
