Wow. The things you miss when you sleep.
Panel 1: Warren comments that Liz is indeed engaged. She says to whom: Anthony.
Panel 2: He identifies his rival as "the guy with the kid", thereby indicating that Liz can't shut up about the people in her life after all. She points out that "the kid" has a name and gender.
Panel 3: She then goes on to explain that the friendship they had grew into something almost like love. Warren's response is to state that it's over between them.
Panel 4: Liz, looking like a morphine addict, says that it never started. Direct Speech. WOW! Lynn must have been paying attention to our snark about her never using it to men. "I'll show them", she said.
Hypothesis: Liz could still set a date on the spot because of a comment Warren made. Warren might decide that he isn't going to stand for being cockblocked. Therese might be the one to make trouble after all.
ETA: Warren's bio is up and indicates that he's leaving Milborough for good. What he's doing is letting Liz off the hook by allowing her to tell him that it's over.