Charliegizmo mentioned statement analysis. We can't refer here to outside blogs on the subject or anything, but we do have Kadoober's transcription and we can analyze that ourselves in our own thoughts.
I don't think I still have Kadoober's transcript open, but there was something about playing with his brothers (as well as his cousins) and bruises.
Thinking of the possible lack of sightings since the 11th, that was a day where we know that the two older brothers were there, reportedly playing with sticks in the garden (with the neighbor's kids).
And we have context of this happening just one week after the incident where one of the brothers goes home with bruises that so concern his father that the father takes photos and goes to the police. The father of EG's boys wants to stop those boys having future visits with EG.
So, what if in the course of playing, or maybe after coming in the house (with Lucas) after playing, one of those boys got a bruise? That would be major for EG. I think that would send her wild, and she might take that out on Lucas.
I now feel I might have a working theory for the *why* in conjunction with the date of the 11th. In my mind the theories for the 16th felt very weak, but this one feels a lot stronger to me.