The first time that Jack meets Dennis, Liz practically hides her head in her hands at the embarrassment she feels. Perhaps it's the fact that Jack is so obvious in his mocking and Dennis is so oblivious. Or perhaps because looking at them side by side she finds herself feeling... feelings. And not for the man she is currently dating.
The second time Jack almost meets Dennis. Liz is stood by the elevators saying goodbye to Dennis when she sees the next lift arrive and Jack in it. Quickly she says goodbye to Dennis, and walks to meet Jack, leading him in the opposite direction. She doesn't ruminate on the reasons why she doesn't want Jack to see Dennis. It's not like he doesn't know she's still dating him. Maybe it's just she doesn't want to hear the comments that Jack would make about the Pager King. Or maybe it's because the comments Jack would make, are the comments that she's already thinking. And if Jack suggested she dumped Dennis, she'd probably do it.
When Dennis mentions meeting her at work for lunch the next day she quickly shuts him down. Lying, she excuses herself by saying that Jacks been an ass and making her team work through the lunch break in order to improve on their sketches. Dennis doesn't see the lie, even though Liz has never been great at lying, and her acting skills are terrible. Watching Dennis nod his head makes her slightly want to punch him for being such an idiot.
Jack appears in her office at midday and tells her about his new girlfriend. She quickly cuts him off as he says "The sex is... mind-blowing, and she does actually bl-", by saying "That's great Jack." When he suggests a double date, she quickly declines citing Dennis not liking to eat in restaurants where he has to wear a tie and jacket. She's pretty sure that Jack sees right through her as he raises an eyebrow but doesn't argue with her. He just nods his head and leaves.
When she enters Jacks office and tells him that she dumped Dennis, Liz is glad that he just nods his head. Because she's starting to realise that she doesn't loathe Jack as much as she thought she did. And she's also realising that this sort of, kind of, friendship thing they've got on is most probably the most stable and sane relationship she has in her life.
And she quite likes him for it.