The game has Lena explicitly monologue her lust for Axel and desire to "feel safe" take her over when he makes a move on her and five minutes after the fact she snaps out of this and feels like something was possessing her and that something is now gone.
I'm not saying she doesn't enjoy sex with Axel because she evidently does. I'm arguing that she isn't intentionally trying to "make him think he's got a chance with her" because she never has any thoughts to such effect; quite the opposite. Especially in the context "i'll make him want me again and then i'll be the one cheating on him", there's literally no instance in the game of Lena having this sort of thoughts.
Lena potentially agrees to have a coffee with Axel, once he assures her it'd be as nothing but a pair of friends. At no point in the game she is thinking "this will show him that he still has a chance with me". If anything, there are points in the game where she worries or is annoyed that this is what he might still be thinking, because she wants anything but that.
Again, you're attributing to Lena sentiments which are opposite to what she actually displays in the game.
About the only instance that could be considered a "turning point" for Lena's attitude towards Axel is the jealousy and fear she feels when she sees Cindy hitting on him in Ch.11. This might make her want to attract him again, so that she has what she perceives as the stability that she craves. But before that moment, everything she does is with wanting the opposite, that is Axel fucking off and no longer hounding her.
Yes Lena, of course has to express doubts about what she's doing, because this scene has to fit in with a wide range of future possibilities, ones where she falls for him again or becomes his fucktoy or just fucks around with him, and ones where she carries on hating him, and hates herself for succumbing to his charms. Just because she expresses doubts, doesn't mean she's just going to follow the path you claim. But it has to be there, for when she does. It's a common practice for Devs to reuse the same scenes for a variety of different outcomes. So they don't always match exactly those eventual outcomes. And I think that's all you're seeing.
As for Lena, wanting to make Axel want her, so she could cheat him. I never said that was going to happen, only that I want that to happen. And it may still happen, or it might not. The cuck route is still evolving, and Lena is only partially aware herself of what she's actually doing with Ian. So her feelings and actions, could change significantly in the coming updates. And that includes how she gets involved with Axel. Because she's already insinuated to Ian, that Axel's cock was better than his, and Ian got turned on by the possibility of Lena still fantasing about her former boyfriend, and maybe even wanting to do more than fantasise. It's obvious, that Eva intends Axel to be a central part of Ian and Lena's cuckplay. So where that will eventually lead, and how it influences Lena's connection with Axel, is still very much open to debate. Alright you're saying it's not happened so far, so there's no reason to think it will. Well I can say equally, there's no reason to think it wont?
And with the coffee date, it could be construed either way, depending on what you actually want. We don't know what's going to happen. But we do know Eva has created a possible route for Lena to get back with Axel. Can you categorically claim that that isn't going to happen? There is no way, that you can know that? And from my previous experience with GGGB, when Eva opens up a possibility, usually there's a way to get there. Maybe it's not obvious at the moment. But eventually it will probably happen. Which is why I can entertain my ideas regarding Lena and Axel, and hope that they'll eventually come to pass. And if they don't, well it's just too bad. I won't be excessively disappointed.