Lucy has been perfectly happy with the casual sex she's been getting until now.
I think Lucy's issues are far more serious than your description suggests. Her feelings toward Charlotte are very unhealthy and vindictive. For example, she laughs at the thought that MC will be the first guy in years to get Charlotte in bed while her sister is passed-out drunk. She then teases MC with the idea that he should help undress her comatose sister, plus she deliberately draws his attention to her body (legs, dress) as he is carrying her – and just a reminder here, this is a woman who has experienced multiple extreme traumas of sexual violence, including one where she was molested while drugged unconscious, which mirrors her current situation exactly. Lucy justifies this later to Charlotte with the idea that she was only testing MC, but we in the audience know this is just another lie, since immediately after the fact Lucy ridicules and emasculates MC for his honourable behaviour, and then she openly admits to hating her sister and confesses to a long laundry list of deliberate actions taken just to hurt her sister and those around her.
Charlotte has spent the majority of her life without a man in her life. She will be perfectly fine on her own.
Charlotte is just as unsound of mind as her sister, though her particular self-destruction takes on a different character with her alcoholism, self-isolation, obsession with her career and work, complete dehumanization and contempt for men, and extreme overprotectiveness/infantilisation of her daughter. She lives her daily life outside of her protective domestic bubble in a constant state of fear and hypervigilance, and even though she is amused by her daughter's "crushes" and emerging feelings for boys, it is almost a guarantee that the prospect and reality of her daughter actually dating a man would drive her into a paroxysm of self-medication and addiction. Once her fantasy world is punctured by reality, she will be quickly overwhelmed I expect.
The concern is: who is anyone to say that Charlotte isn't right? I'm serious. Her warnings to Kaylah came true almost within hours of their talk, and as I spoke about in my initial thoughts and reactions, this victim-filled world leaves the story with an obstacle so pervasive that it threatens to trap and close the narrative in on itself to an unfortunate degree. I have my own ideas about how it could be resolved, but the developer could have other ways to move things forward, or maybe it won't be dealt with at all (which would be unfortunate). I'm just going to wait and see what happens, and maybe I'll like it, or maybe I won't.