Two video cameras – one in the hall and the other inside the lift – recorded the attack. The man was wearing a black jacket and what appeared to be white surgical gloves and a white dust mask perched on his head.
He was holding what looked like a canister with a nozzle and was spraying as he stepped into the elevator.
Gillespie, who had grocery bags in her arms, turned about 180 degrees and then crouched in an attempt to protect herself, he said.
But the man sprayed her directly in the face and continued to spray her "sort of methodically" over her head and parts of her body. She turned and retreated to the back of the elevator.
Then, Browne said, the suspect pulled out a barbecue-style lighter, used it to ignite a rag in a bottle and then waited for a few seconds before using the flames to set her afire, causing smoke to fill the elevator.
The man backed out as she fell to the floor of the elevator, Browne said, and seemed to pause before tossing the bottle inside the elevator and onto her.
Browne would not comment on the motive in the killing, but said the suspect knew Gillespie.
The Daily News quoted neighbours as saying that Gillespie had been living in the building for years and appeared to be mentally ill.
She often complained that upstairs tenants were stealing from her, the report said.
Residents reported the fire in the lift. “She was screaming at the top of her lungs,” one man told the New York Post.