It has not been established how long LS was in CR/MB's apartment(assuming she was actually there). By MB's account, it would appear to have been brief, like a few minutes, and she wanted to leave. We also have yet to learn how and when she got to JR's apartment (did she just walk a few doors down and knock? Was he outside his door? Did she run into him on the streeet? ) I've seen nothing that gives the timeline from leaving CR/MB's up until JR says he saw her leave. JR's statement of how she came to be at his place, exactly what time this was, what they did, what they discussed, etc... is very important.
However, I agree that someone who simply followed her from Kilroy's or passing on the street probably wouldn't hang around waiting for her, unless he knew her very well, and knew her patterns.