I think I found a plot hole
...from season one.
It was snowing the night Lula died. The police ruled a suicide, and she was thought to be alone.
But it was snowing heavily. So there should have been tracks in the snow showing that she had been thrown over the side. (unless the killer wore women's shoes?)
I may be wrong but I believe this is a plot hole. But I have not read the books which may explain this point better.