Burk's body was found in her black Volvo Saturday morning near East 5th Street and Alameda Street.
Police believe Burk was the victim of a botched robbery.
"This case does strike close to home for all of us who have children. This is really a parent's worst nightmare," said LAPD Deputy Chief Sergio Diaz.
The Los Feliz teen left her home on Friday and drove to her mother's office to pick up papers at 2:45 p.m.
Police said Samuel, a parolee, approached Burk at 3 p.m. as she got back to her car on Wilshire Place, just north of 7th Street.
Samuel abducted the teen and tried to get the teen to withdraw money from an ATM in the downtown L.A. area using her credit card, but her card was not set up to take out cash.
She called her father to ask how to get money out of the ATM machine, but he did not detect that she was in harm's way.
"Lily made a number of cell phone calls to her parents. Although she didn't tell them that she was in distress, the subject of those phone calls was her attempt to obtain cash," said Dep. Chief Sergio Diaz of the Los Angeles Police Department.
Burk never came home, and her parents reported her missing Friday night.
Detectives said Samuel ditched her body in the passenger seat of her car. According to the coroner's office, Burk's neck had been slashed and her body was badly beaten. She had head injuries and appeared to have struggled with her attacker inside the vehicle.
Police said Samuel was arrested for drinking in public and possessing a crack cocaine pipe shortly after he allegedly carried out the murder.
His fingerprints were found inside Burk's vehicle.
Police say Samuel is a transient and a career criminal, who was released from state prison last February. They say he has a long rap sheet including assault with a deadly weapon, kidnapping and robbery.
Family and friends are grieving their loss of a girl described as funny, warm and kind.
"She was supposed to be in a play this week," said family spokesman Nick Goldberg.
Burk would have been a senior in the fall at Oakwood School in North Hollywood. Family and friends said she was looking forward to going to college to become a writer. They also say she had planned to volunteer helping the homeless this summer.
Family members said in a statement that they are grateful that police arrested someone so quickly and that this man has been taken off the street.
Samuel has been booked on suspicion of murder and is being held without bail at the Metropolitan Jail. He will likely be arraigned on Tuesday.
Eyewitness News Reporters Melissa MacBride and Carlos Granda contributed to this report.