Don't think its a case of Lima Syndrome since Mr. Kidnapper already had a thing for Sachi before taking her. As for Sachi, I think calling her feelings a case of Stockholme syndrome is a bit simple. Before she was kidnapped, she was being beaten, bullied, verbally/emotionally abused and sexually assaulted and if she stayed where she was at; it would have only been a matter of time until she ended up murdered or committed suicide so I think she figured that being kidnapped by a stranger could not be worse than what she was already dealing with. Kind of like jumping off a sinking ship: there might be sharks, the water might be bitterly cold, might be stranded out in the middle of the ocean for days or weeks but staying on the ship is certain death. So, it would be a simple choice between the unknown or suffering followed by death.
Just my thoughts on the manga.