According to the NYPD, the woman was hit after swerving to avoid a cab that had pulled into the bicycle lane she was riding in.
Her father, Andrew Lyden, said: 'She had only spoken to me the previous day, or the day before, and said "Dad, can you believe your little girl is in New York City?"'
Local authorities said the 23-year-old was forced to swerve into a auto lane when a cab pulled into the bike lane she was riding in.
Madison was rushed to the Roosevelt Hospital after being hit, but attempts to revive her failed.
Felipe D Chairez, 44, has been charged with driving while intoxicated, driving while ability impaired and operating a commercial vehicle with an alcohol reading of 0.04 per cent - 0.06 per cent or less, the New York Police Department (NYPD) confirmed.
Ms Lyden, a swim teacher from Geelong, had only been in the city for a few days on holiday with friends.
Arsenal vs Manchester City
Thus, he is definitely a huge threat for the Manchester City defence, likely to be led by English worldwide John Stones. It's about the mix, when you have a defensive or attacking moment, and I want every player to improve in this way.
Beer cans were found in the garbage truck and he was arrested at the scene, local media reported.
Dozens of bystanders rushed to Lyden's aid.
The advocacy group Transportation Alternatives says Lyden's death underscores the need for protected bike lanes. Her latest stop had brought her along with friends to NYC, in what was presumably supposed to be the trip of a lifetime.
Ms Lyden had been working at a Waurn Ponds aquatic centre for nearly two years.
Lyden also left behind a twin sister, who was at a loss for words to describe the depths of her heartbreak.
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