The jacket baffles me. As you note, she may have left it at JR's, and we just haven't heard about it. If she took it to Sports, she'd have taken it off, I think ... hung it on the back of a chair, perhaps. She could have tied it around her waist, but IDK if she'd have done that, being a fashion major. Maybe somebody took her jacket from Sports and doesn't want to admit it, under the circumstances. A lot of clothes disappear from our local high school ... some kids take what they find.
I actually thought that her jacket might show up in the landfill even if LS didn't. If the jacket didn't have pockets, maybe she kept her phone in her wristlet and just had it out for whatever reason. That's weird, too, though ... since CS said LS didn't use it after leaving SW. Maybe she was waiting for a call/text or using it to check the time? Or did she have a watch on? Actually, having her cell out might have been instinctive ... which would make her leaving it even stranger.
I'm really not sure why it is assumed to be a jacket in the first place. The initial description (and missing person report) had her with a white long-sleeve button down.