Cat won't have a relationship with Lawson after BB. I get the impression she entered the house to get a start on a new phase of her life. As soon as she entered the house, it is as if the outside world became insignificant. She wanted to test herself in this new environment, and made sure she backed off men who had already expressed interest in one of the other girls or those she would have to compete for (i.e. Jake). In a kooky way, Lawson was a safe object because he's only 22, and just not very attractive. Unlikely to ever have had to, or wanted to dissuade an admirer. He's already taken by someone outside who can never intervene, so Cat can practice her newly-single ways on him. No one else in the house was interested in him, so he represents a free run. And if he knocks her back, it's because he already has a girlfriend, nothing to do with Cat herself. I think that was the basis of Cat's attraction to him, and her obsessive personality and need to control this relationship has taken over in unexpected ways.
As for Lawson, I see him absolutely basking in the attention of a smart, very attractive woman who'd never look at him twice on the outside. She's seeing something very special in him, and Lawson really wants to know what that is. He's not in love with her, he's in love with himself. It's only when he's been drinking that he actually seems to want to touch her. If only he knew that Cat's working out her own feelings about herself, and they form the most significant influence on her behaviour, and really have little to do with him at all.
Once she leaves the house, it will be the beginning of the next phase of Cat's life. I think she will be quickly taken up by some guy who thinks gorgeous and slightly unhinged women are hot.
That's it for my amateur psychology time. And standard disclaimer: Lawson's behaviour is worse. And I am only still writing about this because there isn't anything else of much interest going on with BB right now. It's their fault.