1. Ivy puts photo from Axel apartment on her Peoplegram and "accidentally" forgets to tell about it to Lena, although she could definitely predict her friend's reaction
Or perhaps she didn't tell Lena precisely because she knew her friend didn't want to hear anything about her ex-boyfriend at that moment. What would be the point of this? "
Hey look, this is a photo of me in Axel's apartment." You'd need to be
really socially dense to think it's a good idea.
2. Ivy pushes Lena to work with Axel
3. Ivy doesn't come with Lena to Axel, although she knew how awkward it would be for her. And "accidentally" she can come after they finished the photoshoot.
Ivy advised Lena to work with Axel after Lena told her that she and Axel talked things out and both moved on. As far as she could tell at this point, it was perfectly reasonable advice. And yes, she got stuck and wasn't able to arrive at the arranged time, but again, as far as she's told, that's nothing to freak over. Lena and Axel are allegedly on friendly terms.
4. In the gym when talking with Lena Ivy "accidentally" tells Lena that nothing happened, right? wink, wink, nudge, nudge
Or it's a simple and genuine question. Again, as far as Ivy knows, Lena and Axel have both moved on, and Lena has no interest in sex with Axel -- she potentially has a new boyfriend and also repeatedly told Ivy she doesn't want any relationship with Axel.
It's not so much a "wink wink nudge nudge" but "But nothing happened, right, you've told me yourself you don't want him, so why are you busting my proverbial balls over simply being late?"
5. Ivy wants Lena to keep fucking Axel, even when she realizes that she looked really happy with Ian.
Ivy tells Lena she doesn't have to freak out so much over sleeping with Axel, or feel so guilty about still wanting his cock. If she wants, she can sleep with him and Ian both. Which is true. It's something for Lena to decide, Ivy isn't Ian's keeper.
Ivy is many things, but she isn't an idiot and she knows Lena well.
If it rattles like a snake and slithers like a snake, is it a snake?
Given that Ivy isn't an idiot then
why would she want to be a "snake" for her best friend? If she wanted to mess Lena's life then she gets many more opportunities, like spiking her drink with drugs when Lena tells her she doesn't want any. But instead she respects Lena's choice. So, if she demonstrates that she does care and respect what Lena wants, why do you presume she'd act exactly opposite?
I'm not saying your theory is impossible, but it'd be very much an asspull given what overall we're shown when it comes to Lena/Ivy. As it is, Ivy is a fairly rare sort of character, someone who is sexually open but respectful of others and actual good friend. Turning her into mustache twirling villain would be quite a disappointment, because these are dime a dozen and there's at least two in ORS alone already.