Well watching the episode now I noticed something else. It appears that Joe was up to something with her because not only did Al mention that she was last seeing leaving the shelter with him but he claims that teh dog Bofus was scratching to go out but a quick scene clearly shows the dog lying peacefully at the old couple's feet and Joe lead him away. So it's clear that he meant something but Sam inercepted him when he insisted that Cissy stay and let him go after the dog. And that was most likely what led to Lisa. In the original history it was Joe letting to dog out that got her killed.
All things consitered though looking back I kind of like the idea of Lisa now. A pysho jealous ex-gf is a pretty cool idea.
One thing that puzzles me about this is that when Joe offered to go with Sam to get the dog, why the heck did Sam turn him down?
I don't think Joe could have been the original killer, because why would he follow Cissy back to her house? Then again, why would Lisa? Clearly the "thing" she went to get was the dog, and Joe was seen letting the dog out but he seems like a normal person, I don't buy that he would have any reason to kill Cissy, Lisa's the much better suspect, even in the OH.