Long time lurker....just throwing in some ideas.
We still have sketchy details about when dad left for his out-of-state-job, or if he was even there for sure when this all happened. The thought has crossed my mind, being that LE has been hush-hush on details regarding dad's work and location at the time, that is there a possibility that something happened to little Lucas prior to dad leaving for work? Could there be a chance that in the middle of another spat between dad and EG that something happened to Lucas and dad took the body (i hate even saying that) across state lines to dispose of? In that case, he could be anywhere. I am praying this isn't even a possibility.
If dad were involved, maybe LE felt the best way to get them to talk would be to separate them, put one in jail, keep an eye on the other and maybe eventually one would talk out against the other. Just a thought.
And regarding the infamous pull-up. I taught in an at-risk preschool in Kansas, and all children had to be potty trained prior to coming to school. I can understand a pull-up at bedtime, but not a 3:00 in the afternoon. Unless a child has a medical reason to need a pull-up, I can's see why an average 5-year old would need one during the day unless it is due to laziness on a parent's part or in many cases they revert back when major changes in their life happen, such as new sibling, move in location, abuse (or in Lucas' case all the above)
One last thing I keep thinking about too, is that fact that if EG was alone, 24/7, with a one-year-old and a sick 5-year-old (if he was sick) that she would have to be exhausted. She could have been way out of patience and very angry at dad for leaving her for weeks on end to be responsible for two small children. Maybe she snapped and harming Lucas was (in her sick mind) a way of revenge toward dad. Regardless of how tired us moms get and how low on patience we run, the majority of us would never take it out on a child, but obviously EG wasn't of the majority.