Lau competed in a race at the national championship in Montchavin-Les-Coches in 2003 and made his debut in the Telemark World Cup two years later on January 24, 2005 . In the same year he was junior world champion in giant slalom in Beitostølen in 2005 in the Junior World Championships, fourth in the Classic Sprint and fourth in the Classic 14. The 2006 season was mixed because he mostly ends up in midfield except in Schweitzer Mountain Resort he was third in the Sprint World Cup . In 2007 he only contested the World Cup in Bad Hindelang, Germany, and was on the podium for the second time in the Sprint World Cup . At his first World Championship in Thyon in 2007 , he won the bronze medal in the Classic Sprint.
In 2008 Lau was able to establish himself among the world's best and won a world cup race for the first time. In 2009 he managed to win another World Cup race and further podium places. The 2009 World Championship in Kreischberg was unsuccessful. Because he finished fifth in the giant slalom, eleventh in the classic and sixth in the classic sprint. In 2010 and 2011 he won seven races and achieved additional podium places. In 2011 he crowned his career with an overall World Cup victory. At the 2011 World Championships in Rjukan he was world champion in the classic sprint, seventh in the classic race and 12th in the giant slalom.