Here's the subtext related to Paul's blackmail arc, as I see it. And, of course, a certain amount of subjective interpretation is unavoidable when discussing subtext. Bear in mind that I'm playing the Sharing route. Of course, it's necessary for Lisa to have cheated on Danny with Viv, in order to trigger the blackmail, so the Cheating route is also active in my playthrough, but the Sharing route is the primary route which I'm playing. The subtext of the game may be different on different routes.
- Danny - Lisa's Relationship with Danny on the sharing route is pretty good, at the point in the game when the blackmail starts, and it has actually been getting better as the story progresses. So there is good reason to believe that Lisa wouldn't want to lose Danny, or to have their relationship damaged in any way. Also, it should be remembered that they have only engaged in sharing, not in any sort of open relationship in which they fool around with other people separately, and they have not even discussed an open relationship (so far). So Lisa has no reason to believe that Danny would be okay with her fucking other people when he isn't there, and especially not without his permission. Is it possible that Danny would be okay with what she and Viv have been doing? Yes, it's possible. But Danny has already shown his capacity for jealousy once, at the swim meet, so it's not a safe assumption that he would be okay with it, especially since Lisa didn't ask him about it before doing it, didn't include him, and hasn't told him about it after the fact. She has, in fact, kept it from him. She has cheated on him, and there's really no other way to look at it. And she clearly knows that she has cheated, because she hasn't told him and is afraid of him finding out. This is made clear in her dialogue with Viv in her bedroom, but I think that it should be made clearer and emphasized more, rather than just relying on subtext. If Lisa has been keeping this secret from Danny (She has.), and is afraid of him finding out (She is.), then this is definitely a motive - possibly a strong motive - for her to submit to Paul's blackmail.
- Luca and Viv - Yes, I'm including Viv in this, and not only because she's Lisa's "partner in crime" in cheating on Danny. Lisa is becoming more and more invested in both Viv and Luca as the story unfolds. She thinks that Luca is a sweet kid, but that he lacks confidence and that he's too withdrawn. She recognizes that he's highly intelligent, and she wants to see him do well. She tries to encourage him, both in his studies and in physical exercise, and it almost certainly follows that she wants him to have a good opinion of her. She also has compassion on his and Viv's situation of apparently having been abandoned by Luca's father. She sees that Luca loves his mother and tries to support her through her feelings of abandonment and her drinking problem, and that he doesn't want his mother to be worried about him. And she also understands why Viv is worried about her son, given that he also feels abandoned and is shy and withdrawn. And, sex aside, she has also begun to care about Viv, even going so far as to stand up to Riggs on her behalf. So it should be easy to see why she wouldn't want Luca to find out about her affair with his mother. He might feel betrayed by her, and lose his good opinion of her, and all of the work she has done to encourage him and bring him out of his shell might be undone. So she needs to keep her affair with Viv a secret, in order to protect Luca, but also to protect herself and her investment in Luca. And, she also needs to protect Viv. Since she has no idea how Luca might react to finding out about her and his mother, she can't be sure that he wouldn't also feel betrayed by his mother, or might feel that his mother betrayed his father. Sure, he called his father a bastard, the one and only time in the game that he mentioned his father, but that doesn't mean that his feelings about his father aren't still very complicated. Lisa can't possibly be sure of how he would react, either to her or to Viv. And she knows that Luca is the only thing Viv has left, and pretty much the only reason she goes on living. She can't risk possibly being the cause of a breakdown in their relationship, not if she cares about both of them.
- Jo - In the introduction to the game, we are told that Jo is Lisa's dearest friend (Though Gina is also a very close friend.), and that they have been friends for many years. And we also know that Jo is very close to Danny. At the swim meet, it was made clear that Jo does not look kindly on Lisa cheating on Danny. Despite her longstanding and close friendship with Lisa, she isn't going to tolerate Lisa turning into a cheat, assuming that she finds out about it. The swim meet also makes it very clear that Lisa values Jo's good opinion of her, and feels terrible at the thought of their friendship being harmed. Well, if Paul's blackmail route is active, then Lisa has cheated on Danny with Viv. She doesn't want Jo to find out, anymore than she wants Danny to find out.
So, in order to protect her relationship with Danny, her relationship with Jo, her relationship with Luca, Viv's relationship with Luca, and possibly her relationship with Viv (Since Viv might blame Lisa if Luca turns against his mother over the affair.), Lisa can't risk her cheating coming to light. She actually has a shit-ton to lose. She has to keep the affair a secret, and she has to do whatever is necessary to that end.
Of course, she's making the wrong choice. What she should do is to tell Danny and Jo and Luca the truth and take whatever consequences might come. But it's easy to understand (and completely believable) why she wouldn't choose that option. So now she has to go on submitting to Paul's blackmail, until she can come up with a plan to turn the tables on him and get free.
This is my reading of the subtext of the game. I could be reading it wrong, but I don't think I am. And I do think that this is more than enough motivation for Lisa's choice to submit to the blackmail. However, I don't think that this should be left in the subtext. I think that it should be spelled out more clearly in the dialogue and Lisa's internal monologue. Some of the explanation is there, in her conversations with Viv and Paul, but I think that it should be made clearer, for the benefit of anyone who may not have picked up on the subtext.
For the record, you should feel free to argue against me. I'm not allergic to people disagreeing with me. And, if I were, that would be my problem, not yours.