The method by which that would probably happen is, as clio_1 said, fairly simple; it seems fairly likely that Liz would, after months of dealing with the fact that the man she thought had all the romantic answers was a morose, emotionally-stunted, distant, self-pitying, sunken-chested, humorless, charmless, witless doofus whose sole 'virtue' is his canine loyalty to her parents, would find herself in much the same situation as a woman she'd thought of as a devil for confusing her with a gold-digger and "cheat" on a man whose fairly obvious revulsion stems from the fact that she's not a talking blow-up doll whose only function is to tell him he's great. I'd like to think that she'd realize that she and Thérèse have more in common than she thought before having her affair with a human being from the get-go but I'd be willing to wait for that admission when she finally confronts her whiny shmuck husband about how, to coin a phrase, she'd made him up.
That being said, it's fairly obvious that the same Elly who didn't see that April shouldn't actually forgive a thug who'd wanted to kick the shit out of her because his dad played harmonica and didn't believe April's accusations because Kortney flattered her would, of course, take Anthony's part at first. Were John around to validate her need to not pay attention to her surroundings, Liz would be screwed because Mommy would be able to walk around with her brain asleep spouting nonsense. Without John to hide facts from her, things would, of course, end differently; she'd examine the evidence of her senses with great reluctance but, sooner or later, she'd see that she saw things in Anthony that weren't there because she wanted to and because he made her feel good about being self-serving and silly.
The realization that she'd more or less wasted her life getting everything wrong because being right was too much like work would hurt at first but, well, she'd survive. As for Anthony, he'd end up being viewed as most of us see him: a weak, crouching figure who doesn't have what it takes to cope in this world and thus must be thrown crumbs by his betters. The Elly of the new order would want better than that for her family so he'd be the cautionary example we thought that Lynn was making him into in the first place.