In May 2011, Mark and another man brutally beat Lossiah with a stick and stole his wallet and car keys. He died 12 hours later at the hospital.
A jury found Mark guilty of first-degree murder in November.
District Judge John Dean handed down a life sentence for the murder, which will be followed by a three-year prison sentence for a conspiracy charge.
Mark will serve 30 years from the day the murder happened, plus the three-year sentence before he will be eligible for parole.
Lossiah's relatives said he was polite, kind and joyful. He played drums and sang at powwows and small music venues.
Daniel Tso, Lossiah's uncle, talked about his nephew's final moments. Neighbors overheard Lossiah begging his attackers to stop and paramedics found him surrounded by blood and brain matter, pleading for help.
"He was even polite to Mr. Justin Mark. He said "Please stop.' And when he was found by EMTs he said "Please help,'" Tso said. "Until his dying day he did what he was taught."
Born in Torreon, Lossiah was the oldest of five brothers. He was raised by his grandmother and enjoyed traveling the country and meeting new people.
Lossiah was 40 at the time of his death. He worked at the Walmart in Durango and lived alone in a small apartment
Marquita Mark, Justin Mark's sister, apologized to the Lossiah family during the hearing.
Marquita and her brother were raised in Sanostee by their grandparents because their parents were alcoholics. Justin Mark turned to alcohol at a young age, he dealt with problems by hitchhiking to Farmington to drink, she said.
"He took the wrong path. He chose that path for himself," she said.
Tom Clark, Mark's attorney, said his client was not the primary aggressor in the attack. He said Mark cooperated with police after his arrest and directed them to evidence.
"He comes from a sad and tragic background that is not uncommon," Clark said.
While addressing the court, Mark made what appeared to be a reference to a homosexual relationship with Donovan King, who also is charged with first-degree murder in the case.
Mark said his boyfriend, King, killed Lossiah. Mark asked the court to shorten his sentence and give him credit for talking to police and leading them to evidence after his arrest.
"I am not the one who killed Kevin Lossiah," he said. "If it weren't for my help the state would not have found (Lossiah's) wallet. You should give me credit for that."
The state didn't have to prove whether Mark or King was the person to fatally strike Lossiah. A person can be convicted of felony murder if a person dies while the suspect is committing a felony.
King, a 23 year old from Red Valley, Ariz., is awaiting trial.
The New Mexico Supreme Court will rule on whether King's statements to police after his arrest can be used in court. During his interview with Farmington police, he told investigators he didn't want to talk at the moment because he was intoxicated. Police continued to question him.
Mark also made comments to police after his arrest that couldn't be used in court because Mark asked for an attorney and said he didn't want to answer questions but police questioned him anyway.
Prosecutors convicted Mark without relying on his statements.