There was a balcony at Lula's flat. Her adopted brother wanted the whole inheritance and had already killed Charlie, another adopted son by pushing him in to a quarry. Martin Shaw who was the old lady's brother tried to stop them adopting Lula as he suspected that the brother John had murdered Charlie and was afraid the same would happen to Lula, which it did.
Lula had made contact with her birth brother (same father, different mother) but he resisted meeting her because of the effect it would have on his mother. John found out she had made contact with her brother and that she had done a will leaving him all her money.
He therefore killed her as he wanted all the money. He was unable to find the will, but Strike realised where it was when the old lady said she had brought back some mementos from Lula's flat, so he pretended to go to the loo in the old lady's house and found the will in Lola's handbag. He had been told that designer bags could have their linings removed when he was with the model who he slept with and who offered him drugs which were hidden in her bag.
The brother John wanted Strike to say that her real brother killed her, but Strike was too clever.
I thoroughly enjoyed it and hope that my long-winded and a bit rambling explanation helps you to understand it.