Ms Lummis said the obsession was such that the defendant had tried to hire a hitman to kill the woman's previous boyfriend.
The plans never eventuated because the prospective killer went to prison on unrelated charges, the court heard.
On the night of June 30, Mr Hawe-Wilson, Ms Hawe, Tu and others had been drinking at the Panmure house in which they were all living.
By midnight, everyone had gone to bed except for Tu, who went for a walk.
When he came back at 2am, he had decided to kill Mr Hawe-Wilson.
"Mr Tu, who had been staying at the same house for several days, found a hammer in a kitchen cupboard and crept quietly into the bedroom to make sure Crystal and Mr Hawe-Wilson did not wake. He stood over the sleeping couple and administered two if not three fatal blows to [the man's] head," Ms Lummis said.
The force of the blows was so strong, she told the jury, that pieces of the teenager's skull were embedded in his brain.
"He didn't stand a chance. His death was so sudden he did not wake; in fact he barely moved," she said.
Ms Hawe slept through the entire incident and Tu allegedly returned the hammer to the cupboard where he found it.
Ms Lummis said he re-entered the bedroom about five hours later and climbed into bed between the dead body and the sleeping woman.
She woke with him allegedly trying to pull down her jeans and chased him out of the room while yelling for Mr Hawe-Wilson to help.
It was only when she returned to the bed and she saw the blood that she knew something was wrong.
Emergency services arrived shortly afterwards and Tu allegedly explained to a constable "he had no alternative but to end Mr Hawe-Wilson's life to save his own".
In later police interviews, he called it an "assassination", Ms Lummis said.
While the Crown accepted Tu had significant mental-health difficulties, they rejected the assertion he was insane at the time of the alleged murder.
Defence lawyer Peter Tomlinson said that was the prime issue on which the jury needed to focus.
"There's no dispute that the defendant caused the death of Mr Hawe-Wilson, no dispute at all. But what the defence does say to you is that at the time he caused that death, he was so mentally impaired . . . he was incapable of knowing what he did was morally wrong," he said.
Mr Tomlinson said his client had spent a long period in the Mason Clinic after the killing while he was unfit to stand trial and he urged the jury to pay close attention to evidence about Tu's mental state.
The trial before Justice Christian Whata is set down for three weeks.
