As a junior, Tyler was a gifted sportswoman, focussing on swimming at junior high school and later triathlons. She moved into criterium events while living in Florida and in 1988 made the move to velodrome events. In 1990 she trained and raced in Australia, initially living in New South Wales. During this period she married track rider Martin Vinnicombe. The pair were training at the Trexlertown Velodrome facility in Pennsylvania in 1991, when Canadian drug testers at the request of their Australian counterparts recorded a positive drug test for Martin Vinnicombe. This ended Martin's career but the following year Lucy took up Australian residency and in the 1993 national championships in Alice Springs represented the state winning the sprint and 10 km scratch race.