The motive the Rs were suggesting for LHP was money. Patsy stresses LHP's financial stress and the fact that she had asked to borrow money.
What Patsy wasn't able to do was explain how the sexual aspect of the crime would have involved LHP. As far as I am concerned, what rues out a sexual predator intruder is that the sexual aspects of the crime were hidden. A sexual predator/killer DISPLAYS his victims and advertises the sexual activity that has taken place or mutilates his victims in a sexual way. But JB's sexual assault wasn't discovered until the autopsy, and the Rs reacted defensively to being informed of it, rather than horrified and wanting to find the person who abused their daughter at all costs.
LHP and her family were all tested for a match to the DNA, and writing as well. NO match.
I believe the Rs had a list of people they planned to suggest to LE as possible perps. Among them were their friends the White's, one of JR's former employees and LHP. The White's and presumably the former employee (Merrick) had the education and means to defend themselves vigorously, and of course, the Rs knew there was nothing to really link them to the crime.
But LHP was much more vulnerable. There was still nothing to link her to the crime, but she was in a much less favorable position to defend herself against them.
JR set the wheels in motion within minutes of bring his daughter's body up from the basement- he looked Det. Arndt in the eye and said "This is an inside job". This DESPITE the RN and suggestion of a "small foreign faction". The Rs couldn't settle on which way they wanted to aim the blame, so they threw out as much as they could to see where it would stick.
It didn't really stick anywhere, did it? NO one they "suggested" was found to have any link at all to the crime, the body, the house, the RN.