]Why would she do that? Is she

a)just teasing her friend
b)afraid that her friend will offend Mr. Darcy, and wants to rush her away; or
c)is she at work match-making, showing off Lizzy's talents to him?

The latter two of those reasons, I think. She shows earlier in the chapter that her idea of matrimony is for security, and interest for her friend might prompt her to foreward the match as much as she can.
Also, Mr Darcy is a guest at her home, and she would definitely wish not to offend him, as he is higher up on the social scale. However, her way, I found to be almost uncivil, and IMO, seemed to bother Elizabeth.