The 38-year-old was killed by Detroit police who returned fire after four officers were shot Sunday afternoon.
Moore's grandmother, aunt and sister say they are devastated and shocked by what happened inside the Northwest District.
The suspect's grandmother, Paula Hodges says "I've been knowing him for years and it's just so out of character for Lamar to have just walked into the police station and went on a rampage like that. He didn't seem to have any problems. We talked all the time. He was always jovial. It's just so out of character."
His aunt, who did not give her name said "I did not believe it. As a matter of fact, it's still, I'm still not digesting it right now."
Moore's family says the last time they saw him was just two hours before the shootings.
His sister also did not give her name, but she described the encounter like this: "He came in. He seen the baby. Just normal. He was normal. He's never had a problem." Moore's sister went on to say, "Nothing was abnormal. He wasn't upset about anything. He's not a violent person. Nothing adds up here."
She says that shortly after the shooting, she went by her brother's house. She was very emotional as she told Action News that the police were already there. "I went by his home myself and the crime scene van was already by his house. That was at 3:20 today. They were already knocking on his door and knocking at the neighbors door and they were in his house, so how do you say, I mean, they gotta show me a tape."
Moore's sister was referring to the tape from the cameras inside the Northwest District. Moore's grandmother says she also wants to see the tape, "Yes, I would like to see it. I mean it's just so hard for me to believe that he did this."
Moore's aunt says the family has many questions, but that they "just want some justice. Just like their families want justice, I want justice for my brother."