With over 300 awards from various competitions, Ljubek is the most decorated Croatian canoeist and one of the most successful Croatian athletes. He was a multiple national champion and a member of the national team in canoeing on calm waters, and won his first medal at the World Championships in Belgrade in 1975.

His next success was at the 1976 Olympic Games in Montreal, when he won gold and bronze in the C-1 1,000 metres and C-1 500 metres, respectively, and repeated his success at the 1984 Olympics in Los Angeles, winning gold and silver in the C-2 500 metres and C-2 1,000 metres. He won ten medals at the world championships in the period from 1975 to 1985: one gold, one silver and two bronze medals in the C-1, and three gold, two silver and one bronze medal in the C-2. He also achieved a great triumph at the 1979 Mediterranean Games in Split, where he won three gold medals.

In the early 1990s, he assumed the position of president of the Croatian Canoe Federation and participated in the founding of the Croatian Olympic Committee, where he held various positions. Since 2001, the Croatian Olympic Committee’s Lifetime Achievement Award in Sports has been named after him.