Blue, I had to add that this question really made me smile, because only a female would ask it. Ask any young single man if he'd have sex for 2 weeks with a woman, having seen only her picture and that she was good looking, and I'd bet 98% would say yes, without hesitation. The 2% who hesitated would be wondering if she was psychotic and likely to murder them in their sleep or go Lorena Bobbitt on them.
Since Lynn is portrayed as moderately attractive, 20, and not actually violently psycho, and "S" is portrayed as normal, 20, single, and reasonably sexually active, (or at least wanting to be) there is no motivation at all required for him to ask her for 2 weeks' sex. Even if he hates her, it's a good thing. He doesn't have to be fascinated with her, or want to hurt her, or even like her.
He just wants to use her. Plain and simple. He wants sex, she can provide it. She's a free prostitute. The humiliation/subjugation is important, and there are several other layers above that as you saw, and as I provide in my other answer. But they're not necessary for most men to identify with the basic motivation.
I always find it a bit funny when a woman assumes a man must really like her, or be fascinated with her, or want to hurt her, when all he wants is her body. Sometimes, to paraphrase Freud, a penis is just a penis.
Does anyone think I'm way off here?
I suspect that if women had evolved so that there would be no personal consequences to sex, they might feel the same way more often than they do.
Personally, after about 1 to 2 weeks, I would start to form an emotional attachment, or failing that, a strong repulsion. So the 4 weeks wouldn't have worked for me. But that's just me-- everyone's different on that score.