I often take notes while reading through the case information and in this, I noticed a few things that are pretty obvious.
This killer most likely was someone from within her daily world or see often. It also would seem that he has knowledge of her building, apartment and security system so it could have been another renter or maintenance personnel or something like that. I see why they would question the Fiance of course being he may have had access to her apartment. This person was close and knew her and most likely developed an obsession. From the reading, she was full of life, happy, funny and pretty. All the great things that people like to be around. For someone like a Psychopath or a sexual sadist, it’s like putting drugs in front of an addict and telling him to look but not touch. They can’t resist the compulsion.
By the details of how Laurie was murdered, it’s plausible that this may have been motivated by sexual gratification. As I don’t have all the details, that’s all I can really discern at this point. Strangulation could have occurred during a sexual assault as we have seen with many lust murderers throughout the 60s through the 80s. It’s also possible the killer did not sexually assault the body as we saw with the cases of BTK and Richard Speck. Both compulsive serial sexual sadists. Most of their victims died from strangulation. Gerald Brudos also strangled most of his victims for sexual gratification. All have similarities with this unsolved case. Just some food for thought.