How did he find her and how/why did he do so in the 2.5 blocks between the corner of 11th and college and the entrance to SW? Without being noticed by JR or anyone else on Btown's main street and given what we've been told about the geography (that you can't wait at 11th and college for someone to appear)?
How/why did he find her there (wherever there is) without ever attempting to enter SW (which would be captured on camera and probably reported by multiple people) or 5N (which would be reported by other POIs)? And when LS had no phone? Note that any contact between those at SW and him would be reflected on his phone.
And what happens next? Who else is involved/knows? If no one, how does he do it alone? Remember the facebook picture - he isn't much bigger than LS, so this is not a big, strong guy. How does he get in and out unnoticed and get back in time and in a state sufficient to make everything seem normal for his roommate who he drives to class at noon, for HT, who he gets the keys from 2 hours later, for LE, who he files the missing persons report with 1-2 hours after that, and for LS's parents, who he calls?
If others know, why are they (or all of them) a) protecting a murderer, and b) risking criminal prosecution and possible jail time in the process?
Either way, how does he do this without doing anything that would make LE talk him up (or not call him 'cooperative'), like recording suspicious messages on LS's phone or using his car (if it has onstar, for example; how does he keep evidence of her off the car?) or leaving prints?
PS Why is there no evidence that he was seen anywhere that night? Where are the people talking about problems in their relationship? Where are the people talking about how he always seemed like a bad guy, or jealous, or angry, or violent? Why are the other POIs not pointing fingers at him?