Panel 1: Liz sulks because Mike changes plans on her mid-stream because she's sort of stupid really. She lacks the understanding of social norms that forces Mike to ditch her so he can be Canadian Content Ross Geller.
Panel 2: Her feeble-minded rage makes her think that she was invited under false pretenses. Mike tries in vain to get the dodo to understand.
Panel 3: He needs to not really talk to Martha alone and hands Liz pocket change to spend at Shopper's Drug Mart for the next hour.
Panel 4: Liz goes full-on Lucy Van Pelt because he wants her to be understanding for a buck.
Summary: It fits that Liz is a dope here. Not only does she rely on Mike and her idiot mother as a source for the straight dope on Martha, she never bothers realizing that they'd be as self-serving describing someone else as they are when talking about her.
Also, on Monday, howtheduck will show you that while Martha might have changed, Mike is still the same indecisive knob who can't think of anything to say to her when she's a real person.