Ms Lyden suffered severe trauma injuries and was taken to the Roosevelt Hospital, where she was pronounced dead.
The cyclist and the truck collided next to a bus stop near a sign for the Tavern on the Green.
Jorge (who declined to give his last name), a doorman on 65 Central Park West, was across the road when the accident happened.
“It was in the middle of rush hour, there were cars going and cars coming,” he said. Then he heard honking and screaming.
“The truck went on top of her,” he said. “I saw people screaming. They were saying, ‘Please wake up, people, please, call 911,”’ he said.
Visibly upset, Jorge said he had never seen anything like it in his life.
Melissa Kennelly was walking by when she passed the accident and saw two cars with trash strewn between them.
A local news crew said the friend she was with tried to resuscitate her.
Mr Tsourovakas said officers were at the scene, where the investigation was ongoing.
“Our investigation is still in its infancy,” he said.
The truck driver has been taken into custody and police are testing to see whether the driver was under the influence of any substance, another NYPD spokesperson has confirmed.
No charges have been laid.
Ms Lyden’s family has been notified of the tragedy.
City of Greater Geelong chief executiveMartin Cutter on Sunday expressed deep sorrow over her death.
“Madison commenced with the city as a learn-to-swim teacher, lifeguard and receptionist in March 2017, working at our Leisurelink, Waterworld and Kardinia Pool facilities around Geelong,” he said.
“Madison was a valued and respected team member and she will be greatly missed.
“The city is offering all appropriate support services to our staff who might be affected during this very difficult time.”
A DFAT spokesperson said officials were providing consular assistance to the family.
“For privacy reasons we will not provide further comment,” the spokesperson said.
A transportation advocacy group said it was “a crash waiting to happen” because “lazy and entitled drivers” are parking, dropping people off and idling in bike lanes.
Transportation Alternatives said Ms Lyden’s death “underscores the need for every major street in New York City to have a safe, protected space to travel by bike”.
With Goya Dmytryshchak and AP