Not surprised that Lizzy hasn't come back to Running Man. She was good in her first few appearances as a guest, but when she became a regular she was getting so little screentime as to be almost invisible in the episodes. Plus the ratings weren't great at the time. Hardly surprising she didn't stick around.
I wouldn't mind seeing her as a guest every once in a while, but they've got a good thing going with the regular cast now that there's need to mess with it.
Yeah, many people including myself have pointed out that Lizzy pretty much disappears by the end of her run, it's pretty hard not to notice. I think she got booted off the show while she was away promoting with AS because they never actually mention her leaving, she just disappeared after her final episode. Anyway, it was probably the right choice given the success of RM afterwards.
As a fan of hers, I would obviously like to see her on the show again, I wouldn't really care if it was as a guest or a member. She stated pretty clearly in one of her interviews that she wants to be back on the show, so I don't think it was her choice to not be on RM. It kind of sucks that she hasn't even appeared as guest even though she's expressed interest. There are just too many unknowns to really get worked up about it though.
As for a new member messing up the chemistry of the show, I'm not sure what to think anymore. Originally I was against adding another member and then I was for it, right now I'm not sure it would make any difference. In most newer episodes there's just so much focus on the guests and going through the missions. The interactions between the members, which originally carried the show, have taken a back seat to guiding the guests and going through whatever games are being played that day (without much talking or competitiveness among the members), episodes like 130 aside.