Liz is Rob’s connection to Laura. He is clearly not over her. Losing her makes him completely re-evaluate his life. He uses Liz to try to understand what is going on with Laura. This shows that he still loves Laura and wants to be with her, even though he is having trouble expressing it.
Liz comes across as a good friend in Hornby's work. In the end, she is going to support Laura, as she is Laura's friend. However, she does recognize Rob's genuine good heart and his sense of decency. Realizing that a breakup rarely brings out any person's positive qualities, Liz is able to talk to Rob about the breakup and provide some level of "reconnaissance" to Rob about how Liz is doing after the breakup. Yet, in the end, Liz is not going to support Rob over Liz. Rob realizes this, but still Liz is able to come across as trying to be as supportive to two decent people in a difficult time for both of them. She does show herself to be a relatively fair person at a point where two people are in the throes of actions that are unfair to one another. I think that she also shows herself to be a relatively calming influence on both Rob and Liz, who are fairly far off from calm given both the intensity of their relationship and the breakup that follows. In true Rob fashion, I think that Liz would have to be on a "Top 5 List of most stable people in Hornby's work."