Münter began racing in California in 2001 in the Allison Legacy Series. She debuted with a seventh-place finish. In 2002 Münter made the move to Mooresville, North Carolina, widely regarded as the center for NASCAR racing. In 2003, she had her first start in the NASCAR Weekly Racing Series at South Boston Speedway, she finished ninth. She made her first speedway start in 2004 at Texas Motor Speedway and set a new record when she qualified fourth, the highest qualifying effort for a female driver at the track. It was also her first super late model race; she finished seventh. In 2006, she had her first full-time season in a race car. In her fifth race of the season, she had one of the biggest races of her career when she finished fourth, setting a new record at Texas Motor Speedway for the highest finish for a female driver in the history of the 1.5 mile speedway. Later that year, Leilani became the first woman to qualify in the 45-year history of the Tony Bettenhausen Classic at Illiana Speedway in Indiana. In 43 stock car starts, Münter scored 19 top tens and 9 top five finishes. At the end of the 2006 racing season, she was set to make the move into the ARCA Series in 2007, a stepping stone series into NASCAR's top three series. In December 2006 she completed her ARCA rookie test at Daytona International Speedway. She was 24th quick of 59 race cars testing that day in a race car prepared by Andy Hillenburg, a retired driver who owns Fast Track Racing School, where Münter once worked at as an instructor.