I'm late, but the killer's motives are revealed in the scene with the injured mumbling man. He wanted to cover up stealing a painting and would murder anyone with any knowledge of it. The ex-lover (the girl in the wall) had written about the stealing in a letter to the old woman. He also tried to kill his wife (I assume she's alive) because he thought she had read the letter.

"What does it do?"
"It doesn't
do
anything. That's the beauty of it."