At Lucas lodge, when Lizzy sets about showing Darcy that she knows that he is spying on her conversations, Charlotte interrupts their conversation, almost rudely, IMO, asking Lizzy to play and sing.

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?