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I don't believe they have had the affair because when Eve is talking to Addison and basically confesses her motives to Addison before he blows her cover, she states that they sat up and talked all night, to which Addison asks, you sat up and talked, and she responds that she wants a "run of the play contract." I took that to mean that she was not going to sleep with him until she got a wedding ring first.

There may have been somewhat of an emotional affair, but not a physical one. Eve manipulated Lloyd into coming over in order to plant that seed in Karen's head.
If it were a full-out affair with contemplation of marriage, no way would Karen have been so quick to forgive and reconcile with him.

I'm not completely convinced that there was no affair. I'm basing this on Karen's narration (she is saying this while we see her lying in her bed alone in the dark, with an obviouly depressed air). She reads the narration right before that phone call from Eve's room owner (?) calling Lloy's help to comfort the supposedly distressed ingenue
"It seemed to me I had known always that it would happen - and here it was. It felt helpless, that helplessness you feel when you have no talent to offer - outside of loving your husband. How could I compete? Everything Lloyd loved about me, he had gotten used to long ago"
It seems to me that the narrator would not have made such a big thing of it if nothing had happened

• But you can't have her again as costume designer, Mr. Hitchcock!
• Really, Peggy? Give me Head!

Thanks for your responses, everyone!

Eve was bluffing, all the way. As sh2836 pointed out, the "nugget of truth" was Eve and Lloyd sitting and talking all night but that's it.

FA - Imo, no. As with many sociopaths, there is often a small nugget of truth in what they say. That's why they are such convincing liars. Especially back in the 50's, it really was to Eve's advantage to play upon Lloyd's sympathy, and allude to wild adventures to follow later. Her main goal was a run of the play contract, and Eve intended to lead him on until that was accomplished. Iow, Imo they really did sit and talk all night, with Eve shamelessly flattering Lloyd's probably big ego.
Someone asked why Lloyd's demeanor changed so drastically from the out of town opening to the Sarah Siddons award dinner. If I had to guess, Eve had to drop Lloyd like a hot potato after Addison's ultimatum. Addison knew way too much for Eve to cross him, and she was forced to give up her idea of marriage to Lloyd.

Yes.
Pay no attention to the man behind the curtain.

Did they have sex? I don't think so. I'm pretty sure Eve was just jumping the gun with Addison; it's not like she's a big truth teller.
I do think Lloyd got emotionally involved with the "poor kid" and felt guilty (and stupid).
I do wonder, what happened between the part where he rushes to the "poor kid's" aid, and the awards show (where he appears to be as disgusted by Eve as Margo, Karen, and Bill).

What does your response have to do with the OP, pray tell?

Now go home and get your beep in shine box! Good fellas 1990
Uh baby U 4got to pull out. 9 months later, can U pull this ucking baby outta me, do that @ least!