Levente Balatoni started to ski in 1928 in the colors of MAC. He competed in both Alpine and Nordic skiing, as well as in athletics and boxing. With the MAC team he won the Hungarian cross-country skiing championship in 1934 and 1935. As a university student, he joined the BEAC team in 1936 and won his only individual championship title there, when he finished first in the Nordic combined championship in 1937. He also played and coached the ice hockey team of BEAC.
Balatoni took part at the 1936 Winter Olympics in Garmisch-Partenkirchen, where he was chosen as the Hungarian flagbearer at the Opening Ceremony. He was not so lucky in the competitions. In the Alpine combined, he fell and was injured during the downhill run, was unable to finish the race, and had to withdraw from the slalom section and ski jumping. After World War II Balatoni left Hungary and settled in Great Britain.