Her partner Darren Harwood and best friend Charlotte Piccaver went to her aid only for them both to be stabbed to death, Lincoln Crown Court heard.
Ozen, 41, claimed self-defence but a jury disagreed. He was ordered to serve a minimum of 27 years in prison.
The jury failed to reach a verdict on a further charge alleging Ozen tried to murder Miss Wright.
Mr Justice Flaux said: “This was a brutal attack on two young people who at the time were unarmed.”
He added: “The lack of respect shown to your victims during your evidence leads me to suspect you have little remorse.”
During the trial the jury heard Ozen had sublet a room in the flat he lived in above a shop in Red Lion Street to Miss Wright after losing his job.
But they argued after the Turkish-born British national failed to pass her rent money on to the owner of the property.
Investigating officer Det Ch Insp Martin Holbey said emergency services arrived to find a “horrendous scene” with a woman dead in a bedroom, a man dying and another woman stabbed in her arm and back.
Miss Piccaver, 26, was pronounced dead at the scene on 21 April and Mr Harwood, 26, died later in hospital.
In a statement, Miss Piccaver’s family said the guilty verdict was a relief.
“Charlotte was a loving, loyal daughter to all her family and friends,” they said.
“Her death leaves a void that will never be filled but the guilty verdict allows us to start looking forward, rather than being in limbo, and we thank everyone involved in the case.”
This article originally appeared on bbc