That's where her fear of repercussions for neglect/abuse might come in. If he is accused of murder, she could be too if she admits to LE that she left Lonzie in WRE's hands, ill and injured. Plus, WRE knows about LLB and CB's drug involvement and could use that info to implicate them. I think both LLB and CB hoped that by appearing to believe his story, he would stay silent about other things that could land them in jail.
I think LLB is all about LLB, and she will do anything to stay out of jail.
I think LLB may have figured out that Lonzie died after she talked to the cop that pulled her coworker and her over. She acted (to me) like she needed time to get her own story straight because she wasn't expecting the kidnapping story, and I think she told the truth to her coworker when she asked to be dropped off further from the apartment so she could see what was happening first. Was it really a kidnapping or worse? If he told her something bad happened that he needed to take care of, but didn't specify what it was, I can see her reactions being "natural" to her. Lie, deny.
This would possibly explain why Chief Hackney said she was cooperating but that she also lied from the beginning.
It also might explain why she hasn't yet been officially named as a suspect in Lonzie's disappearance.
And JMO, I think it explains her very self-destructive behavior since then. She partied before Lonzie disappeared, now she's just wanting to get wasted, and she's not being very careful. To me that looks like a drug addict displaying guilt, fear, regret, and grieving.
Of course this is all JMO and speculation.
I think maybe WRE dumped the car there because that's all he had time for and it was a familiar place in the dark. Maybe he was in that area earlier in the day to deliver drugs, or get drugs or like we've speculated, he parked there to avoid being found by police because he had missed a court appearance and was expecting a warrant to be issued because of it? IDK
Again, just speculating based on what we know. I wish we knew more